Results 21 to 30 of about 859 (75)

Bender–Knuth Billiards in Coxeter Groups

Forum of Mathematics, Sigma
Let $(W,S)$ be a Coxeter system, and write $S=\{s_i:i\in I\}$ , where I is a finite index set. Fix a nonempty convex subset $\mathscr {L}$ of W. If W is of type A, then $\mathscr {L}$ is the set of linear extensions of a poset,
Grant Barkley, Colin Defant, Eliot Hodges, Noah Kravitz, Mitchell Lee   +4 more
doaj   +1 more source

Enumeration of bigrassmannian permutations below a permutation in Bruhat order

, 2010
In theory of Coxeter groups, bigrassmannian elements are well known as elements which have precisely one left descent and precisely one right descent.
A Björner, A Lascoux, L Balcza, M Geck, Masato Kobayashi, N Reading   +5 more
core   +1 more source

Orthogonal roots, Macdonald representations, and quasiparabolic sets

Forum of Mathematics, Sigma
Let W be a simply laced Weyl group of finite type and rank n. If W has type $E_7$ , $E_8$ or $D_n$ for n even, then the root system of W has subsystems of type $nA_1$ .
R. M. Green, Tianyuan Xu
doaj   +1 more source

Asymptotic behavior of word metrics on Coxeter groups.

Documenta Mathematica, 2011
We study the geometry of tessellation defined by the walls in the Moussong complex MW of a Coxeter group W . It is proved that geodesics in MW can be approximated by geodesic galleries of the tessellation.
G. A. Noskov
semanticscholar   +1 more source

On the growth rate of ideal Coxeter groups in hyperbolic 3-space

, 2015
We study the set G of growth rates of of ideal Coxeter groups in hyperbolic 3-space which consists of real algebraic integers greater than 1. We show that (1) G is unbounded above while it has the minimum, (2) any element of G is a Perron number, and (3)
Komori, Yohei, Yukita, Tomoshige
core   +1 more source

Commensurators of parabolic subgroups of Coxeter groups

, 1996
Let $(W,S)$ be a Coxeter system, and let $X$ be a subset of $S$. The subgroup of $W$ generated by $X$ is denoted by $W_X$ and is called a parabolic subgroup. We give the precise definition of the commensurator of a subgroup in a group. In particular, the
Paris, Luis
core   +2 more sources

Affine Bruhat order and Demazure products

Forum of Mathematics, Sigma
We give new descriptions of the Bruhat order and Demazure products of affine Weyl groups in terms of the weight function of the quantum Bruhat graph.
Felix Schremmer
doaj   +1 more source

The flat closing problem for buildings

, 2014
Using the notion of a strongly regular hyperbolic automorphism of a locally finite Euclidean building, we prove that any (not necessarily discrete) closed, co-compact subgroup of the type-preserving automorphisms group of a locally finite general non ...
Ciobotaru, Corina
core   +1 more source

Linear syzygies, flag complexes, and regularity

, 2014
We show that for every positive integer R there exist monomial ideals generated in degree two, with linear syzygies, and regularity of the quotient equal to R. Such examples can not be found among Gorenstein ideals since the regularity of their quotients
Constantinescu, Alexandru, Kahle, Thomas, Varbaro, Matteo   +2 more
core   +1 more source

On Normal Subgroups of Coxeter Groups Generated by Standard Parabolic Subgroups

, 2005
We discuss one construction of nonstandard subgroups in the category of Coxeter groups. Two formulae for the growth series of such a subgroups are given.
M. R. Bridson, M. W. Davis, M. W. Davis, N. Bourbaki, Światosław R. Gal   +4 more
core   +1 more source