Longest element of a Coxeter group information

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...

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...

to the longest element of a Coxeter group. There are a number of analogies between algebraic groups and Weyl groups – for instance, the number of elements...

Schubert cell, or equivalently the longest element of a Coxeter group. Longest element of a Coxeter group Poincaré duality Hatcher, Allen (2002). Algebraic...

longest element of a Coxeter group. The number of cells in a given dimension of the Bruhat decomposition are the coefficients of the q-polynomial of the...

=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...

length of a Weyl group element. A longest element of a Coxeter group is both important and unique up to conjugation (up to different choice of simple...

quasi-isometry invariants. Length function Longest element of a Coxeter group J. W. Cannon, Geometric group theory, in Handbook of geometric topology pages 261–305...

orthogonal group as well. It equals the identity if and only if the characteristic is 2. It is the longest element of the Coxeter group of signed permutations...

the theory of Coxeter groups, the symmetric group is the Coxeter group of type An and occurs as the Weyl group of the general linear group. In combinatorics...

taken as a unit for hypervolume. Coxeter labels it the γ4 polytope. The term hypercube without a dimension reference is frequently treated as a synonym...

 33–34, §3.1 Congruent transformations. Coxeter 1973, p. 63, §4.3 Rotation groups in two dimensions; notion of a fundamental region. Trujillo-Pino, Agustín;...

unions and intersections. Motivated by a problem of defining partial orders on the elements of a Coxeter group, Armstrong (2009) studied antimatroids...

Killing form has level twice the dual Coxeter number. Equivalently, level one gives the inner product for which the longest root has norm 2. This matches the...

It is a special case of a chord, namely the longest chord for a given circle, and its length is twice the length of a radius. Disc: the region of the plane...

} depending on an element w {\displaystyle w} of the infinite symmetric group S ∞ {\displaystyle S_{\infty }} of all permutations of N {\displaystyle \mathbb...

generating set (BSGS) of a permutation group Todd–Coxeter algorithm: Procedure for generating cosets. Buchberger's algorithm: finds a Gröbner basis Cantor–Zassenhaus...

the Euler line" (PDF). Forum Geometricorum. 11: 231–236. MR 2877263.. Coxeter, H.S.M. "Introduction to Geometry 2nd ed. Wiley, 1961. Minda, D., and Phelps...