In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections. The product depends on the...

In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic...

the Coxeter graph, Coxeter groups, Coxeter's loxodromic sequence of tangent circles, Coxeter–Dynkin diagrams, and the Todd–Coxeter algorithm. Coxeter was...

In mathematics, the longest element of a Coxeter group is the unique element of maximal length in a finite Coxeter group with respect to the chosen generating...

a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group...

element of W) and W S = W {\displaystyle W_{S}=W} . The pair ( W I , I ) {\displaystyle (W_{I},I)} is again a Coxeter system. Moreover, the Coxeter group...

In group theory, the Todd–Coxeter algorithm, created by J. A. Todd and H. S. M. Coxeter in 1936, is an algorithm for solving the coset enumeration problem...

the four-dimensional measure polytope, taken as a unit for hypervolume. Coxeter labels it the γ4 polytope. The term hypercube without a dimension reference...

generated by some subset of S). A Coxeter matroid is a subset M of W/P that for every w in W, M contains a unique minimal element with respect to the w-Bruhat...

=e_{1}e_{2}\cdots e_{n}.} This is both a Coxeter element of sorts (product of reflections) and a longest element of a Coxeter group in the Bruhat order; this is...

or 5-orthoplex. Coxeter, Regular Polytopes, sec 1.8 Configurations Coxeter, Complex Regular Polytopes, p.117 H.S.M. Coxeter: Coxeter, Regular Polytopes...

pentachoron, pentatope, pentahedroid, tetrahedral pyramid, or 4-simplex (Coxeter's α 4 {\displaystyle \alpha _{4}} polytope), the simplest possible convex...

Coxeter element s 0 ⋅ s 1 ⋯ s n − 1 {\displaystyle s_{0}\cdot s_{1}\cdots s_{n-1}} in S ~ n {\displaystyle {\widetilde {S}}_{n}} is a Coxeter element...

corresponds to the identity element of the Weyl group, and the dual top-dimensional cell corresponds to the longest element of a Coxeter group. There are a number...

mathematics, the Coxeter complex, named after H. S. M. Coxeter, is a geometrical structure (a simplicial complex) associated to a Coxeter group. Coxeter complexes...

two reduced words of a Coxeter group to represent the same element. Sometimes, this is also called Matsumoto's lemma. A Coxeter group is a group that admits...

n Coxeter group has n mirrors and is represented by a Coxeter–Dynkin diagram. Coxeter notation offers a bracketed notation equivalent to the Coxeter diagram...

alternately labeled (checkerboarded) facets, with Schläfli symbol {3,3,31,1} or Coxeter symbol 211. It is a part of an infinite family of polytopes, called cross-polytopes...

of the group algebra of a Coxeter group. The Hecke algebra can also be viewed as a q-analog of the group algebra of a Coxeter group. Hecke algebras are...

Coxeter 1973, § 1.8 Configurations Coxeter, Complex Regular Polytopes, p.117 Conway, Burgiel & Goodman-Strauss 2008, p. 406, Fig 26.2 Coxeter, Star...

Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter...

gotaf). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by...

The Goldberg–Coxeter construction or Goldberg–Coxeter operation (GC construction or GC operation) is a graph operation defined on regular polyhedral graphs...

hyperbolic Coxeter groups, or 4-prisms, of rank 5, each generating uniform honeycombs in hyperbolic 4-space as permutations of rings of the Coxeter diagrams...

as HM7 for a 7-dimensional half measure polytope. Coxeter named this polytope as 141 from its Coxeter diagram, with a ring on one of the 1-length branches...

Honeycombs under advisor Coxeter, completes the basic theory of uniform polytopes for dimensions 4 and higher. 1986 Coxeter published a paper Regular...

as HM5 for a 5-dimensional half measure polytope. Coxeter named this polytope as 121 from its Coxeter diagram, which has branches of length 2, 1 and 1...

BσB is determined by the length of σ as an element of W. The dimension is maximized at the Coxeter element and gives the unique open dense double coset...

unoriented diagram (a special kind of Coxeter diagram), the Weyl group (a concrete reflection group), or the abstract Coxeter group. Although the Weyl group...

the simply laced finite Coxeter groups, by the same diagrams: in this case the Dynkin diagrams exactly coincide with the Coxeter diagrams, as there are...