Hendrina, died in 1999 children Susan Thomas, and a son, Edgar HaroldScottMacDonald Donald Coxeter ... Canadian vegetarians Category People from Harpenden ar de HaroldScottMacDonaldCoxeter es HaroldScottMacDonaldCoxeter fr HaroldScottMacDonaldCoxeter it HaroldCoxeter he ht HaroldScottMacDonaldCoxeter nl HaroldCoxeter pl HaroldScottMacDonaldCoxeter pt HaroldScottMacDonaldCoxeter sv H.S.M. Coxeter zh ...Infobox scientist name H. S. M. Donald Coxeter box width image Coxeter.jpg image width 240px caption ... youth, Coxeter composed music and was an accomplished pianist at the age of 10. ref name Roberts Roberts, Siobhan, King of Infinite Space Donald Coxeter, The Man Who Saved Geometry , Walker & Company .... Coxeter went up to Trinity College, Cambridge Trinity College , University of Cambridge Cambridge ... Roberts ref name MacTutor MacTutor Biography id Coxeter ref In 1932 he went to Princeton University ... as a Procter Fellow. ref name MacTutor In 1936 Coxeter moved to the University of Toronto, becoming ... hyperbolic tessellation s. He also inspired some of the innovations of Buckminster Fuller . Coxeter ... polyhedra 1954 . Since 1978, the Canadian Mathematical Society have awarded the Coxeter James Prize ... Coxeter, Longuet Higgins, Miller, Uniform polyhedra , Philosophical Transactions Phil. Trans. 1954 ... Coxeter. John Wiley, 1995, ISBN 0 471 01003 0 Bibliography Chandler Davis and Erich W. Ellers, editors The Coxeter Legacy Reflections and Projections. American Mathematical Society, 2006, ISBN 0 8218 3722 2 See also Boerdijk Coxeter helix Coxeter functor Coxeter group Coxeter number Coxeter Dynkin diagram Coxeter James Prize Coxeter Todd lattice Coxeter s loxodromic sequence of tangent circles LCF notation Todd Coxeter algorithm Tutte Coxeter graph References Reflist External links MathGenealogy id 12555 http www.ams.org notices 200310 fea coxeter.pdf H. S. M. Coxeter 1907 2003 , Erich W. Ellers ... more details
ScottMacDonald may refer to ScottMacDonald musician , member the Canadian band Spoons ScottMacDonald actor , American actor Scott McDonald , Australian footballer hndis Macdonald, Scott ... more details
refer Harold Richard Scott 1887 1969 , English Commissioner of the London Metropolitan Police from 1945 to 1953 Harold Russell Scott, Jr. 1935 2006 American stage director and actor Harold Scotty Scott , American vocalist with The Temprees trio HaroldScott actor , British actor See also Harry Scott disambiguation hndis Scott, Harold ... more details
Sir HaroldMacdonald Steward 8 September 1904 &ndash 3 March 1977 was a United Kingdom British consulting engineer and Conservative Party UK Conservative Party politician. He was the Member of Parliament MP for Stockport South UK Parliament constituency Stockport South for nine years, and later became Leader of Liverpool City Council . Engineering training Steward was born in Rainhill , near St Helens, Merseyside St Helens . He went to the local secondary school and to Cowley School in St Helens. He went into business at the age of 14, continuing to train in engineering at the St Helens Municipal Technical College. Steward later became a production engineering manager, and later still a development engineer he worked for the same company all through. During the Second World War he was seconded to work on radar research, and after the end of the war, served on an inter services mission to former enemy countries. Involvement in politics Already interested in politics he had won a Conservative Party prize for public speaking before the war , Steward was appointed a Justice of the Peace for Lancashire in 1951 and fought Liverpool Edge Hill UK Parliament constituency Liverpool Edge Hill at the United Kingdom general election, 1951 general election later that year . This was a near marginal constituency, although in the result, Labour improved its majority in the constituency against the national trend. Steward was elected to Liverpool City Council in 1953. Byelection candidate In January 1955, Steward was selected from 60 applicants to be Conservative candidate for Stockport South UK Parliament constituency Stockport South where a byelection was pending after Sir Arnold Gridley, 1st Baron Gridley Arnold Gridley was given a peerage. In a straight fight with a Labour candidate ... Steward, Harold ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Steward, Harold Category 1904 births Category 1977 deaths Category Conservative ... more details
Infobox person name ScottMacDonald image Scottmacdonald.jpg image caption Macdonald in Star Trek birth date 1964 nationality American occupation Actor years active 1993 present ScottMacDonald Born 1964 is an United States American actor . He is best known for his recurring roles as Captain Manning on short lived series Threshold TV series Threshold , Burley from HBO series Carniv le , and as List of minor recurring characters in Star Trek Enterprise Dolim Commander Dolim from Star Trek Enterprise , and as the title character from 1996 horror film Jack Frost 1996 film Jack Frost . He grew up in Libby, Montana and graduated from Washington State University and received an Master of Fine Arts MFA in acting theatre from the California Institute of the Arts . He has also done stage theatre stage acting, including on Broadway theatre Broadway . Films Fire in the Sky 1993 ... as Dan Walton A Rats Tale 1996 ... as Rudi Rake Rat voice Jack Frost 1996 film Jack Frost 1996 ... as Jack Frost Character voice William Psychspeare s The Taming of the Shrink 1998 ... as Bulbis The Rat Pack film The Rat Pack 1998 ... as Tourist Babylon 5 A Call to Arms 1999 ... as First officer Bad City Blues 1999 ... as Mack Seven Girlfriends 1999 ... as Scot, the Jogger Jack Frost 2 Revenge of the Mutant Killer Snowman 2000 ... as Jack Frost voice Straight Into Darkness 2004 ... as Deming Jarhead film Jarhead ... s Law 1 episode External links imdb name id 0531924 name ScottMacDonald memoryalpha ScottMacDonald http www.webcitation.org query?url http www.geocities.com actorzinc Scott MacDonald.html&date 2009 10 25 12 01 44 ScottMacDonald at Actorz Inc. Persondata Metadata see Wikipedia Persondata . NAME Macdonald, Scott ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1964 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Macdonald, Scott Category American film actors Category American television ... alumni Category 1967 births fr ScottMacDonald ... more details
Other people2 HaroldScott disambiguation HaroldScott Infobox actor name HaroldScott image RIVERSIDE SHAKESPEARE COMPANY HAROLDSCOTT as BRUTUS.jpg caption Scott as Brutus in the Riverside Shakespeare Company production of Caesar , The Shakespeare Center , 1984 birthdate 6 September 1935 birthplace Morristown, New Jersey deathdate 16 July 2006 deathplace Newark, New Jersey Harold Russell Scott, Jr ... Robertson title HaroldScott, 70, Director Who Broke Racial Barriers, Dies url http query.nytimes.com ... Bot retrieved archive archivedate 2008 05 14 ref Life and career Scott was born in Morristown, New Jersey . His mother was a housewife and his father, Harold Russell Scott, Sr., was a general practitioner ... External links ibdb 16106 Harold Russell Scott, Jr. IMDb name 779212 HaroldScott Persondata Metadata see Wikipedia Persondata . NAME Scott, Harold Russell, Jr. ALTERNATIVE NAMES SHORT DESCRIPTION ... OF DEATH Newark, New Jersey DEFAULTSORT Scott, Harold Russell, Jr. Category 1935 births Category ... 2006 accessdate 2008 06 02 ref Scott first became known for his work as an electrifying stage actor ... ref Scott was educated at Philips Exeter Academy and Harvard. He had a career as a stage director ... Award for acting in Jean Genet s Deathwatch in 1959, Scott also played on Broadway in The Cool World. Scott was chosen by Elia Kazan to be an original member of the Repertory Theatre of Lincoln ..., Scott returned to Off Broadway to play Brutus in a modern dress production of Shakespeare s Caesar ... 14 March 1984 accessdate ref Scott staged numerous innovative productions in New York and at regional ... Robeson on Broadway twice in 1988 and again in 1995. Scott also directed the twenty fifth anniversary ... Theatre in New York it then broke box office records at the Kennedy Center in Washington, DC. Scott ... of the Arts date accessdate 2008 06 02 ref Scott was head of the directing program the Mason Gross ... 2006, Scott directed his final play, Yellowman , an examination of black on black prejudice, at the Cincinnati ... more details
Other people2 HaroldScott disambiguation unreferenced date November 2010 Sir Harold Richard Scott , Royal Victorian Order GCVO , Order of the Bath KCB , Order of the British Empire KBE 1887 1969 was Commissioner of Police of the Metropolis Commissioner of the Metropolitan Police Service Metropolitan Police from 1945 to 1953. Scott was born in Somerset , England and raised in Bruton , Somerset . He was educated at Sexey s School and later Jesus College, Cambridge Jesus College of the University of Cambridge . In 1911, he joined the Home Office as a civil servant , where he worked in various capacities including Secretary to the Labour Resettlement Committee 1918 1919 and Chairman of the Prison Commission England and Wales Prison Commission 1932 1939 . With the outbreak of World War II , Scott s work took on a more military capacity, as he joined London s Civil Defence Administration until he was appointed as Permanent Secretary of the Ministry of Aircraft Production in 1943. In late 1944, the Home Secretary Herbert Morrison asked Scott to accept the post as Metropolitan Police Commissioner when the war was over. The appointment in 1945 caused a stir in police circles Scott was the first Commissioner without a police or military background since Sir Richard Mayne who had been a lawyer when appointed . Scott s administration background served him well in some of the more managerial aspects of the Commissionership, and he managed some considerable cost savings for the Met. He also ... Persondata . NAME Scott, Harold ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1887 PLACE OF BIRTH DATE OF DEATH 1969 PLACE OF DEATH DEFAULTSORT Scott, Harold Category 1887 births Category ... of genial PC George Dixon. Scott presided over several high profile cases during his time with the Met ..., Scott introduced a British Police Cadets police cadet training scheme for young people aged between 16 and 18. Scott retired in 1953, and thereafter wrote several books related to crime and policing ... more details
Infobox planet minorplanet yes width 25em bgcolour FFFFC0 apsis name Coxeter symbol image caption discovery yes discovery ref discoverer P. G. Comba discovery site Prescott Observatory Prescott discovered March 7, 1997 designations yes mp name 18560 alt names 1997 EO7 named after HaroldScottMacDonaldCoxeter mp category orbit ref epoch May 14, 2008 aphelion 3.7193981 perihelion 2.5918555 semimajor eccentricity 0.1786559 period 2047.5140421 avg speed inclination 9.27665 asc node 329.18394 mean anomaly 227.06899 arg peri 324.99191 satellites physical characteristics yes dimensions mass density surface grav escape velocity sidereal day axial tilt pole ecliptic lat pole ecliptic lon albedo temperatures temp name1 mean temp 1 max temp 1 temp name2 max temp 2 spectral type abs magnitude 12.9 18560 Coxeter 1997 EO7 is a Asteroid belt main belt asteroid discovered on March 7, 1997 by P. G. Comba at Prescott Observatory Prescott . References Reflist External links http ssd.jpl.nasa.gov sbdb.cgi?sstr 18560 Coxeter JPL Small Body Database Browser on 18560 Coxeter MinorPlanets Navigator 18559 1997 EN2 18561 1997 EY34 MinorPlanets Footer DEFAULTSORT Coxeter Category Main Belt asteroids Category Asteroids named for people Category Discoveries by Paul G. Comba Category Astronomical objects discovered in 1997 beltasteroid stub fa it 18560 Coxeter pl 18560 Coxeter pt 18560 Coxeter ... more details
In mathematics , the Coxeter number h is the order group theory order of a Coxeter element of an irreducible Coxeter group , hence also of a root system or its Weyl group . It is named after H.S.M. Coxeter . ref Citation title The Coxeter Legacy Reflections and Projections last Coxeter first HaroldScottMacdonald authorlink coauthors Chandler Davis, Erlich W. Ellers year 2006 publisher AMS Bookstore ...&dq 22Coxeter number 22 22Donald Coxeter 22 postscript none ref Definitions There are many different ways to define the Coxeter number h of an irreducible root system. A Coxeter element is a product ... orderings produce conjugate elements , which have the same Order group theory order . The Coxeter number is the number of roots divided by the rank. The Coxeter number is the order of a Coxeter element ... for simple roots sub i sub , then the Coxeter number is 1 m sub i sub The dimension of the corresponding Lie algebra is n h 1 , where n is the rank and h is the Coxeter number. The Coxeter number is the highest degree of a fundamental invariant of the Weyl group acting on polynomials. The Coxeter number is given by the following table class wikitable style text align center margin 1em auto colspan 2 Coxeter group Coxeter number h Dual Coxeter number Degrees of fundamental ... of the Coxeter group acting on polynomials form a polynomial algebra whose generators are the fundamental ... invariant then so is h 2 &minus m . The eigenvalues of a Coxeter element ... primitive h th root of unity , sub h sub e sup 2 i h sup , which is important in the Coxeter plane Coxeter plane , below. Coxeter elements Expand section date December 2008 Coxeter elements ... for simple reflections the adjacent transpositions math 1,2 , 2,3 , dots math , a Coxeter element is the n ... 2 pi m math . Coxeter plane File E8Petrie.svg thumb Projection of E sub 8 sub root system onto Coxeter plane, showing 30 fold symmetry. For a given Coxeter element w, there is a unique plane P on which ... more details
In mathematics , a Coxeter group , named after HaroldScottMacDonaldCoxeter H.S.M. Coxeter , is an group ... symmetries. Indeed, the finite Coxeter groups are precisely the finite reflection group Euclidean ..., not all Coxeter groups are finite, and not all can be described in terms of symmetries and Euclidean reflections. Coxeter groups were introduced Harv Coxeter 1934 as abstractions of reflection group s, and finite Coxeter groups were classified in Harv Coxeter 1935 . Coxeter groups find applications in many areas of mathematics. Examples of finite Coxeter groups include the symmetry group s of regular polytope s, and the Weyl group s of simple Lie algebra s. Examples of infinite Coxeter groups ... and Harv Davis 2007 . Definition Formally, a Coxeter group can be defined as a group mathematics .... The pair W,S where W is a Coxeter group with generators S r sub 1 sub ,..., r sub n sub is called Coxeter system . Note that in general S is not uniquely determined by W . For example, the Coxeter groups of type BC sub 3 sub and A sub 1 sub x A sub 3 sub are isomorphic but the Coxeter systems are not equivalent ... yx m yy 1 yx m math . The Coxeter matrix is the n × n , symmetric matrix with entries m sub i j ... such that all nondiagonal entries are greater than 1 serves to define a Coxeter group. The Coxeter matrix can be conveniently encoded by a Coxeter graph , as per the following rules. The vertices of the graph ... by an edge. Furthermore, if a Coxeter graph has two or more connected component graph theory connected ... associated to the individual components. Thus the disjoint union of Coxeter graphs yields a direct product of groups direct product of Coxeter groups. An example The graph in which Vertex graph theory ... 2 k 1 . Of course this only shows that S sub n 1 sub is a quotient group of the Coxeter group described ... groups details Reflection group Coxeter groups are deeply connected with reflection group s. Simply put, Coxeter groups are abstract groups given via a presentation , while reflection groups are concrete ... more details
otheruses4 the 3 regular graph the graph associated with a Coxeter group Coxeter diagram infobox graph name Coxeter graph image Image Coxeter graph.svg 250px image caption The Coxeter graph namesake vertices ... graph Hypohamiltonian In the mathematics mathematical field of graph theory , the Coxeter ... Coxeter Graph ref All the cubic graph cubic distance regular graph s are known. ref Brouwer, A. E. Cohen, A. M. and Neumaier, A. Distance Regular Graphs. New York Springer Verlag, 1989. ref The Coxeter ... and a 3 k edge connected graph edge connected graph . The Coxeter graph is hypohamiltonian graph hypohamiltonian ... graph may exist OEIS id A110507 . Algebraic properties The automorphism group of the Coxeter graph ... ref It acts transitively on the vertices, on the edges and on the arcs of the graph. Therefore the Coxeter ... and any edge to any other edge. According to the Foster census , the Coxeter graph, referenced as F28A ... Graphs Up to 768 Vertices. J. Combin. Math. Combin. Comput. 40, 41 63, 2002. ref The Coxeter ... graph whose don t contains a Hamiltonian cycle , the Coxeter graph is a counterexample to a variant ... path and is verified by the Coxeter graph. Only five examples of vertex transitive graph with no Hamiltonian cycles are known the complete graph K sub 2 sub , the Petersen graph , the Coxeter graph and two graphs derived from the Petersen and Coxeter graphs by replacing each vertex with a triangle ... Census . ref The characteristic polynomial of the Coxeter graph is math x 3 x 2 8 x 1 7 x 2 2 x 1 ... spectrum. Gallery gallery Image Edge excised Coxeter graph.svg The graph obtained by any edge excision from the Coxeter is Hamilton connected. Image coxeter graph 3COL.svg The chromatic number of the Coxeter graph is 3. Image Coxeter graph 11C.svg The Crossing number graph theory rectilinear crossing number of the Coxeter graph is 11. gallery References reflist Category Individual graphs Category Regular graphs fr Graphe de Coxeter ... more details
Summary HaroldScott as Brutus, Riverside Shakespeare Company, 1984. Photo by W. Stuart McDowell. Licensing self GFDL cc by sa 3.0,2.5,2.0,1.0 ... more details
PP1&dq Kaleidoscopes 20Coxeter&pg PP1 v onepage&q &f false Paper 17 HaroldScottMacDonaldCoxeterCoxeter , The Evolution of Coxeter Dynkin diagrams , Nieuw Archief voor Wiskunde 9 1991 233 248 HaroldScottMacDonaldCoxeterCoxeter , The Beauty of Geometry Twelve Essays , Dover Publications, 1999, ISBN 978 0 486 40919 1 Chapter 3 Wythoff s Construction for Uniform Polytopes HaroldScottMacDonald ...see also Dynkin diagram Image Finite coxeter.png 320px right thumb Coxeter Dynkin diagrams for the fundamental finite Coxeter groups File Affine coxeter.PNG 320px right thumb Coxeter Dynkin diagrams for the fundamental affine Coxeter groups In geometry , a Coxeter Dynkin diagram or Coxeter diagram , Coxeter ... a Coxeter group , and Coxeter groups are classified by their associated diagrams. Dynkin diagram s are closely related objects, which differ from Coxeter diagrams in two respects firstly, branches labeled 4 or greater are directed graph directed , while Coxeter diagrams are undirected graph undirected ... Description Branches of a Coxeter Dynkin diagram are labeled with a rational number p , representing ... The Coxeter Dynkin diagram can be seen as a graphic description of the fundamental domain of mirrors ... show the fundamental domains for 2D and 3D Euclidean groups, and 2D spherical groups. For each the Coxeter ..., ignoring 90 degree dihedral angles order 2 . class wikitable width 720 colspan 2 Image Coxeter dynkin plane groups.png 720px BR Coxeter groups in the plane with equivalent diagrams. Domain mirrors ... tilde A 2 math is a doubling of the math tilde G 2 math triangle. valign top Image Coxeter Dynkin 3 space groups.png 360px BR Coxeter groups in 3 space with diagrams. Mirrors triangle faces are labeled ... of the cube. Image Coxeter Dynkin sphere groups.png 360px BR Coxeter groups in the sphere with equivalent ... by their reflection order. Application with uniform polytopes Coxeter Dynkin diagrams can ... can be represented by a Coxeter Dynkin diagram with permutations of markups . Each uniform polytope ... more details
of math H math . See also Coxeter group References J. A. Todd J.A. Todd , HaroldScottMacDonaldCoxeter H.S.M. Coxeter , A practical method for enumerating cosets of a finite abstract group . Proc. Edinb. Math. Soc., II. Ser. 5, 26 34 1936 . Zbl 0015.10103 , JFM 62.1094.02 H.S.M. Coxeter ...In group theory , the Todd Coxeter algorithm , discovered by J. A. Todd J.A. Todd and H.S.M. Coxeter in 1936, is an algorithm for solving the coset enumeration problem. Given a presentation of a group G by generators and relations and a subgroup H of G , the algorithm enumerates the coset s of H on G and describes the permutation representation of G on the space of the cosets. If the order of a group G is relatively small and the subgroup H is known to be uncomplicated for example, a cyclic group , then the algorithm can be carried out by hand and gives a reasonable description of the group G . Using their algorithm, Coxeter and Todd showed that certain systems of relations between generators of known groups are complete, i.e. constitute systems of defining relations. The Todd Coxeter algorithm can be applied to infinite groups and is known to terminate in a finite number of steps, provided that the index group theory index of H in G is finite. On the other hand, for a general pair consisting of a group presentation and a subgroup, its running time is not bounded by any computable function of the index of the subgroup and the size of the input data. Description of the algorithm One implementation of the algorithm proceeds as follows. Suppose that math G langle X mid R rangle math , where math X math is a set of generating set of a group generators and math R math is a set of relation mathematics relations and denote by math X math the set of generators math X math and their inverses. Let math H langle h 1, h 2, ldots, h s rangle math where the math h i math are words of elements ... Coxeter Algorithmus fr Algorithme de Todd Coxeter ru ... more details
File Coxeter helix.png thumb Coxeter regular tetrahedral helix File Boerdijk helical sphere packing.png thumb A Boerdijk helical sphere packing has each sphere centered at a Vertex geometry vertex of the Coxeter helix. Each sphere is in contact with 6 neighboring spheres. The Boerdijk Coxeter helix , named after H. S. M. Coxeter and A. H. Boerdijk , is a linear stacking of regular tetrahedron tetrahedra . There are two Chirality mathematics chiral forms, with either clockwise or counterclockwise windings. Contrary to any other stacking of Platonic solids , the Boerdijk Coxeter helix is not rotationally repetitive. Even in an infinite string of stacked tetrahedra, no two tetrahedra will have the same orientation. Buckminster Fuller named it a tetrahelix and considered them with regular and irregular tetrahedral elements. ref http www.rwgrayprojects.com synergetics s09 p3000.html ref See also Toroidal polyhedron Notes reflist References H.S.M. Coxeter , Regular Complex Polytopes , Cambridge University, 1974. A.H. Boerdijk, Philips Res. Rep. 7 1952 30 The c brass structure and the Boerdijk Coxeter helix , E.A. Lord, S. Ranganathan, 2004, pp. 123 125 http materials.iisc.ernet.in lord webfiles icq8.pdf Eric A. Lord, Alan Lindsay Mackay, Srinivasa Ranganathan, New geometries for new materials , p 64, sec 4.5 The Boerdijk Coxeter helix J.F. Sadoc and N. Rivier, Boerdijk Coxeter helix and biological helices The European Physical Journal B Condensed Matter and Complex Systems, Volume 12, Number 2, 309 318, DOI 10.1007 s100510051009 http epjb.edpsciences.org index.php?option com article&access standard&Itemid 129&url articles epjb abs 1999 22 b8774 b8774.html External links http flickriver.com photos fdecomite 5403437189 Boerdijk Coxeter helix animation Category Geometry Category Polyhedra geometry stub ... more details
infobox graph name Tutte Coxeter graph image Image Tutte eight cage.svg 180px image caption namesake W. T. Tutte br H. S. M. Coxeter vertices 30 edges 45 automorphisms 1440 Aut S sub 6 sub girth 8 chromatic number 2 chromatic index 3 properties Cubic graph Cubic br Cage graph theory Cage br Moore graph ... Distance transitive In the mathematics mathematical field of graph theory , the Tutte Coxeter graph ... 2 sub . The graph is named after William Thomas Tutte and H. S. M. Coxeter it was discovered by Tutte ... of jointly published papers Tutte 1958 Coxeter 1958a . All the cubic graph cubic distance regular graph ... Springer Verlag, 1989. ref The Tutte Coxeter is one of the 13 such graphs. Duads, synthemes, and automorphisms A particularly simple combinatorial construction of the Tutte Coxeter graph is due to Coxeter ... three duads, and each duad belongs to three synthemes. The Tutte Coxeter graph can be viewed as having ... duads that form it. Based on this construction, Coxeter showed that the Tutte Coxeter graph ... may be identified with the automorphisms of the group of permutations on six elements Coxeter 1958b ... the morphemes and synthemes these permutations act on the Tutte Coxeter graph by permuting the vertices .... As Coxeter showed, any path of up to five edges in the Tutte Coxeter graph is equivalent to any other such path by one such automorphism. Gallery gallery Image Tutte Coxeter graph crossing number.svg The Crossing number graph theory crossing number of the Tutte Coxeter graph is 13. Image Tutte Coxeter graph 2COL.svg The chromatic number of the Tutte Coxeter graph is 2. Image Tutte Coxeter graph 3color edge.svg The chromatic index of the Tutte Coxeter graph is 3. gallery References reflist cite journal author Coxeter, H. S. M. authorlink H. S. M. Coxeter title The chords of the non ruled ... Coxeter, H. S. M. authorlink H. S. M. Coxeter title Twelve points in PG 5,3 with 95040 self transformations ... graphs Category Configurations Category Regular graphs fr Graphe de Tutte Coxeter ... more details
Summary Information Description Image of Coxeter s loxodromic sequence of tangent circles. Source self made Date 6 Mar 2008 Location Author User Gandalf61 Gandalf61 User talk Gandalf61 talk other versions Licensing self cc by sa 3.0 GFDL ... more details
In mathematics , the longest element of a Coxeter group is the unique element of maximal length function length in a finite Coxeter group with respect to the chosen generating set consisting of simple reflections. It is often denoted by w sub 0 sub . See Harv Humphreys 1992 loc Section 1.8 Simple transitivity and the longest element, http books.google.com books?id ODfjmOeNLMUC&pg PA15 pp. 15 16 and Harv Davis 2007 loc Section 4.6, pp. 51 53 . Properties A Coxeter group has a longest element if and only if it is finite only if is because the size of the group is bounded by the number of words of length less than or equal to the maximum. The longest element of a Coxeter group is the unique maximal element with respect to the Bruhat order . The longest element is an Involution mathematics involution has order 2 math w 0 1 w 0 math , by uniqueness of maximal length the inverse of an element has the same length as the element . ref name hum16 Harv Humphreys 1992 loc http books.google.com books?id ODfjmOeNLMUC&pg PA16 p. 16 ref For any math w in W, math the length satisfies math ell w 0w ell w 0 ell w . math ref name hum16 A reduced expression for the longest element is not in general unique. In a reduced expression for the longest element, every simple reflection must occur at least once. ref name hum16 If the Coxeter group is a finite Weyl group then the length of w sub 0 sub is the number of the positive root s. The open cell Bw sub 0 sub B in the Bruhat decomposition of a semisimple ... most vertex , which is not central. See also Coxeter element , a different distinguished element Coxeter number Length function References reflist refbegin citation title The Geometry and Topology of Coxeter Groups first Michael W. last Davis year 2007 url http www.math.osu.edu mdavis davisbook.pdf isbn 978 0 691 13138 2 Citation title Reflection groups and Coxeter groups isbn 978 0 521 43613 ... November 2009 Category Coxeter groups ... more details
In mathematics, the Coxeter Todd lattice K sub 12 sub , discovered by harvs txt yes author1 link H. S. M. Coxeter author2 link J. A. Todd last Coxeter last2 Todd year 1953 , is a the 12 dimensional even integral lattice group lattice of discriminant 3 sup 6 sup with no norm 2 vectors. It is the sublattice of the Leech lattice fixed by a certain automorphism of order 3, and is similar to the Barnes&ndash Wall lattice . The Coxeter&ndash Todd lattice can be made into a 6 dimensional lattice self dual over the Eisenstein integers. The automorphism group of this complex lattice has index 2 in the full automorphism group of the Coxeter&ndash Todd lattice and is a complex reflection group number 34 on the list with structure 6.PSU sub 4 sub F sub 3 sub .2, called the Mitchell group named after Howard H. Mitchell . The genus of the Coxeter&ndash Todd lattice was described by harv Scharlau Venkov 1995 and has 10 isometry classes, and all of them other than the Coxeter&ndash Todd lattice have a root system of maximal rank 12. The Coxeter&ndash Todd lattice is described in detail in harv Conway Sloane 1999 loc section 4.9 and harv Conway Sloane 1983 . References citation id MR 0698347 last Conway first J. H. last2 Sloane first2 N. J. A. title The Coxeter&ndash Todd lattice, the Mitchell group, and related sphere packings journal Math. Proc. Cambridge Philos. Soc. volume 93 year 1983 issue 3 pages 421 440 doi 10.1017 S0305004100060746 Citation last1 Conway first1 John Horton author1 link John Horton Conway last2 Sloane first2 Neil J. A. author2 link Neil Sloane title Sphere Packings, Lattices and Groups publisher Springer Verlag location Berlin, New York edition 3rd series Grundlehren ... id MR 0055381 last Coxeter first H. S. M. last2 Todd first2 J. A. title An extreme duodenary form ... dortmund.de preprints 95 07.html title The genus of the Coxeter Todd lattice first Rudolf last Scharlau ... njas lattices K12.html Coxeter Todd lattice in Sloane s lattice catalogue Category quadratic forms ... more details
The Coxeter James Prize is presented annually by the Canadian Mathematical Society . The award is presented to young mathematicians in recognition of outstanding contributions to mathematical research. The first award was presented in 1978. The prize was named in honor of the mathematicians Donald Coxeter and Ralph Duncan James Ralph James . ref http www.cms.math.ca Prizes info cj.html Coxeter James Prize ref Recipients of the Coxeter James Prize 2010 B lint Vir g 2009 Patrick Brosnan 2008 Ravi Vakil 2007 Vinayak Vatsal 2006 Jim Geelen 2005 Robert McCann 2004 Izabella Laba 2003 Jingyi Chen 2002 Lisa Jeffrey 2001 Kai Behrend 2000 Damien Roy 1999 Maciej Zworski 1998 Henri Darmon 1997 Michael Ward 1996 Nigel Higson 1995 Gordon Slade 1994 Mark Spivakovsky 1993 Jacques Hurtubise 1992 J.F. Jardine 1991 K. Murty 1990 Nassif Ghoussoub 1989 Alan Dow 1988 M. Ram Murty 1987 Jonathan Borwein 1986 Edwin A. Perkins 1985 Paul Selick 1984 Mark Goresky 1983 Man Duen Choi 1982 John Mallet Paret 1981 John James Millson 1980 Francis Clarke 1979 David W. Boyd 1978 Robert Moody References Reflist External links http www.cms.math.ca Canadian Mathematical Society Category Mathematics awards Category Awards established in 1978 Category Canadian science and engineering awards ... more details
Harold is an Old English name, meaning heroic leader , same as the title herald . Diminutives of Harold ... disambiguation Harald or HaroldHarold martyr Harold d. 1168 , child martyr and saint Harold Arroyo , Puerto Rican boxer Harold Bloom , American literary critic Harold Craxton 1885 1971 , British composer and pianist Harold Camping b. 1921 , President of Family Radio Harold Faltermeyer b. 1952 as Harold Faltermeier , German musician Harold Ford, Jr. D U.S. Congressman, candidate for U.S. Senate Harold Holt , Australian Prime Minister Harold Houser , American admiral and 35th Governor of American Samoa Harold La Borde , Trinidadian circumnavigator Harold Lloyd , American film actor Harold Macmillan , British Prime Minister Harold Norse , American poet Harold Perrineau , American actor Harold Pinter 1930 2008 , British playwright Harold Wellman 1909 1999 , New Zealand geologist Harold Wilson , British Prime Minister People with the surname HaroldHarold surname , surname in the English language Fictional characters Childe Harold, from the Byron poem Childe Harold s Pilgrimage Harold Allnut , from the Batman comic series Harold Bishop , from the Australian soap Neighbours Harold Crick , the main character from the movie Stranger than Fiction Harold Frost , American Orthopedist and surgeon The Red Green Show Harold Green Harold Green , Red Green s nephew on The Red Green Show Harold ... Engine and Friends Harold Lauder , from Stephen King s The Stand Harold Norse , American poet Harold and the Purple Crayon from the children s books by Crockett Johnson Harold, a living scarecrow from the Scary Stories to Tell in the Dark story Harold Healthy Harold, the automated giraffe mascot of Life Education Australia Harold Lee, from Harold & Kumar List of characters from Total Drama Island HaroldHarold McGrady V from Total Drama Island Harold Hutchins , a main character in Captain Underpants Harold Berman from the Nickelodeon animated show Hey Arnold List of The Power of Five characters ... more details
Refimprove date June 2009 Notability date June 2009 Infobox Defunct Company fate Bankruptcy br Liquidation company name Harold s company logo company type company slogan foundation 1948 defunct 2008 location Dallas, Texas key people num employees 624 prior to bankruptcy filing industry Retail products Mens and Womens clothing revenue homepage Harold s Stores, Inc. was a Dallas, Texas Dallas based chain of traditional, high end classic styled ladies and men s specialty apparel stores. The chain operated 43 stores in 19 mid western and southeastern states in the United States . Prior to its bankruptcy filing, the company employed 624 people. The company was granted bankruptcy liquidation on November 10, 2008 and began liquidating its stores immediately. History Harold s was founded in 1948 in Norman, Oklahoma and was later moved to Dallas, Texas . The chain operated high end mens and women s clothing, usually located in upper class areas and shopping centers in the midwestern and southeastern parts of the United States. On November 10, 2008, the company was granted bankruptcy liquidation , claiming Increased competition and a weak economy have left us no choice but to cease operations. ref http www.foxbusiness.com story markets industries retail harolds going business sale going 992498596 Harold s Going Out Of Business Sale On Now ref References reflist External links http digital.library.okstate.edu encyclopedia entries H HA028.html Encyclopedia of Oklahoma History and Culture Harold s Category Companies based in Dallas, Texas Category Companies established in 1948 Category Companies disestablished in 2008 US retail company stub ... more details
BLP IMDB refimprove only yes date March 2010 Todd MacDonald born 1973 in British Columbia , Canada is an Australia n actor who is best known for his roles on the soap opera Neighbours and the drama series The Secret Life of Us and Rush 2008 TV series Rush . MacDonald s Neighbours stint began in 1996, when he was hired to play Darren Stark Darren , the son of Cheryl Stark Caroline Gillmer . The role of Darren had previously been played by Scott Major briefly in 1993. MacDonald departed the series in 1998, returning for guest appearances in 2004 and 2005, and again in 2007 and 2008. In the early 2000s, MacDonald played the recurring role of Nathan Lieberman on The Secret Life of Us and a supporting role in the drama series Rush 2008 TV series Rush in 2008. MacDonald has also appeared in BeastMaster TV series BeastMaster and Blue Heelers and the movie The Jammed . External links IMDB name id 0531955 name Todd MacDonald Persondata Metadata see Wikipedia Persondata . NAME Macdonald, Todd ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1973 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Macdonald, Todd Category 1973 births Category Australian people of Canadian descent Category Australian soap opera actors Category Living people ... more details
Macdonald Bluffs coor dm 83 15 S 157 50 E is a prominent east facing bluffs between Argosy and Argo Glaciers in the Miller Range , descending to the Marsh Glacier . Mapped by the New Zealand Southern Party of the Commonwealth Trans Antarctic Expedition 1956 58 and named for W.J.P. Macdonald , IGY scientist at Scott Base in 1957. usgs gazetteer antarctica geo stub Category Geography of Antarctica ... more details
for the Scottish mathematician Hector Munro MacDonald Infobox Military Person name Sir Hector Archibald MacDonald born Birth date 1853 03 04 died Death date and age 1903 03 25 1853 03 04 placeofbirth Black Isle , Scotland placeofdeath Paris , France image Image HectorMacdonald.jpg caption Hector MacDonald ... of the Bath K.C.B. br Distinguished Service Order D.S.O. Major General Sir Hector Archibald MacDonald .... The son of a crofter, MacDonald left school before he was 15, enlisted in the Gordon Highlanders ... books?id HvE Pa ZlfsC&pg PA213&lpg PA213&dq hector macdonald military career&source bl&ots ... 6 v onepage&q &f false Harold E. Raugh, The Victorians at War, 1815 1914 An Encyclopedia ... War . ref http books.google.com.au books?id HvE Pa ZlfsC&pg PA213&lpg PA213&dq hector macdonald military ..., from 1765 to the Present , 2001, p.171. ref Career Hector MacDonald was born on a farm at Rootfield ... ref Friseal, A. Eachann nan Cath Gairm, Glasgow 1979 ref . His father, William MacDonald, was a crofter ..., near Inverness . Hector s brothers were the Rev. William MacDonald Jr., known as Preaching Mac , Donald, John, and Ewen. At the age of 15, MacDonald was apprenticed to a draper in Dingwall and then moved .... William Mackay. On 7 March 1870 MacDonald joined the Inverness shire Highland Rifle Volunteers ... substantive major. ref name Raugh213 During the Mahdist War MacDonald commanded a brigade of the Egyptian .... MacDonald swung his men by companies in an arc as the Dervishes charged and by skillful manoeuvring held his ground until Kitchener could redeploy his brigades. When the fight was over MacDonald s troops ..., Hector the Hero ref After Omdurman MacDonald became a household name in Britain. He was promoted ... of the City of Edinburgh , and many Scots felt that MacDonald, and not Kitchener, was the true ... In December 1899 MacDonald was sent to South Africa to command the Highland Brigade Scottish Highland ... in Ceylon now Sri Lanka . Ceylon scandal and suicide Image HectorAMacdonald.jpg thumb Colonel MacDonald ... more details
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