Results 1 to 10 of about 17,658 (187)
A Note on Element Centralizers in Finite Coxeter Groups [PDF]
Journal of Group Theory, 2010 The normalizer $N_W(W_J)$ of a standard parabolic subgroup $W_J$ of a finite Coxeter group $W$ splits over the parabolic subgroup with complement $N_J$ consisting of certain minimal length coset representatives of $W_J$ in $W$. In this note we show that (
Konvalinka, Matjaž +2 more
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Submaximal factorizations of a Coxeter element in complex reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 When $W$ is a finite reflection group, the noncrossing partition lattice $NC(W)$ of type $W$ is a very rich combinatorial object, extending the notion of noncrossing partitions of an $n$-gon.
Vivien Ripoll
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A two-sided analogue of the Coxeter complex [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 For any Coxeter system (W, S) of rank n, we introduce an abstract boolean complex (simplicial poset) of dimension 2n − 1 which contains the Coxeter complex as a relative subcomplex.
T. Kyle Petersen
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Parabolic double cosets in Coxeter groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Parabolic subgroups WI of Coxeter systems (W,S) and their ordinary and double cosets W/WI and WI\W/WJ appear in many contexts in combinatorics and Lie theory, including the geometry and topology of generalized flag varieties and the symmetry groups of ...
Sara Billey +4 more
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On an open problem of Green and Losonczy: exact enumeration of freely braided permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2004 Recently, Green and Losonczy~ GL1,GL2 introduced freely braided permutation as a special class of restricted permutations has arisen in representation theory.
Toufik Mansour
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On non-conjugate Coxeter elements in well-generated reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Given an irreducible well-generated complex reflection group $W$ with Coxeter number $h$, we call a Coxeter element any regular element (in the sense of Springer) of order $h$ in $W$; this is a slight extension of the most common notion of Coxeter ...
Victor Reiner +2 more
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Spacelike Singularities and Hidden Symmetries of Gravity [PDF]
Living Reviews in Relativity, 2008 Marc Henneaux
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Fully commutative elements and lattice walks [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 An element of a Coxeter group $W$ is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. These elements were extensively studied by Stembridge in the finite case.
Riccardo Biagioli +2 more
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Reflection factorizations of Singer cycles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 The number of shortest factorizations into reflections for a Singer cycle in $GL_n(\mathbb{F}_q)$ is shown to be $(q^n-1)^{n-1}$. Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also ...
J.B. Lewis, V. Reiner, D. Stanton
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Gallery Posets of Supersolvable Arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for the longest element whose Hasse diagram is the graph of ...
Thomas McConville
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