Results 41 to 50 of about 17,658 (187)

Coxeter elements and periodic Auslander–Reiten quiver

Journal of Algebra, 2010
27 pages, 10 figures.
Kirillov, A., Thind, J.
openaire   +3 more sources

On Irreducible, Infinite, Non-affine Coxeter Groups [PDF]

, 2006
The following results are proved: The center of any finite index subgroup of an irreducible, infinite, non-affine Coxeter group is trivial; Any finite index subgroup of an irreducible, infinite, non-affine Coxeter group cannot be expressed as a product ...
Qi, Dongwen
core   +3 more sources

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

On the cyclically fully commutative elements of Coxeter groups [PDF]

Journal of Algebraic Combinatorics, 2011
24 pages, 4 ...
Boothby, T., Burket, J., Eichwald, M., Ernst, D. C., Green, R. M., Macauley, Matthew   +5 more
openaire   +3 more sources

Elements with finite Coxeter part in an affine Weyl group

, 2012
Let $W_a$ be an affine Weyl group and $\eta:W_a\longrightarrow W_0$ be the natural projection to the corresponding finite Weyl group. We say that $w\in W_a$ has finite Coxeter part if $\eta(w)$ is conjugate to a Coxeter element of $W_0$.
He, Xuhua, Yang, Zhongwei
core   +2 more sources

Conjugacy Relation on Coxeter Elements

Advances in Mathematics, 2001
Let \((W,S,\Gamma)\) be a Coxeter system, where \(W\) is a Coxeter group, \(S=\{s_1,s_2,\dots,s_r\}\) a distinguished generating set, and \(\Gamma\) the corresponding Coxeter graph. By a Coxeter element \(w\in W\), one means a product \(s_{i_1}s_{i_2}\cdots s_{i_r}\) with \(i_1,i_2,\dots,i_r\) a permutation of \(1,2,\dots,r\).
openaire   +1 more source

Freely braided elements in Coxeter groups, II

Advances in Applied Mathematics, 2004
We continue the study of freely braided elements of simply laced Coxeter groups, which we introduced in a previous work (math.CO/0301104). A known upper bound for the number of commutation classes of reduced expressions for an element of a simply laced Coxeter group is shown to be achieved only when the element is freely braided; this establishes the ...
Green, R.M., Losonczy, J.
openaire   +3 more sources

On the Maximally Clustered Elements of Coxeter Groups [PDF]

Annals of Combinatorics, 2010
We continue the study of the maximally clustered elements for simply laced Coxeter groups which were recently introduced by Losonczy. Such elements include as a special case the freely braided elements of Losonczy and the author, which in turn constitute a superset of the $iji$-avoiding elements of Fan.
openaire   +3 more sources

Polypositroids

Forum of Mathematics, Sigma
We initiate the study of a class of polytopes, which we coin polypositroids, defined to be those polytopes that are simultaneously generalized permutohedra (or polymatroids) and alcoved polytopes.
Thomas Lam, Alexander Postnikov
doaj   +1 more source

An Approach to the Girth Problem in Cubic Graphs

Journal of Graph Theory, Volume 111, Issue 1, Page 17-26, January 2026.
ABSTRACT We offer a new, gradual approach to the largest girth problem for cubic graphs. It is easily observed that the largest possible girth of all n‐vertex cubic graphs is attained by a 2‐connected graph G = ( V , E ). By Petersen's graph theorem, E is the disjoint union of a 2‐factor and a perfect matching M.
Aya Bernstine, Nati Linial
wiley   +1 more source