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Journal of Algebra, 2011 We consider the class of those Coxeter groups for which removing from the Cayley graph any tubular neighbourhood of any wall leaves exactly two connected components. We call these Coxeter groups bipolar. They include both the virtually Poincare duality Coxeter groups and the infinite irreducible 2-spherical ones.
Pierre-Emmanuel Caprace +1 more
exaly +4 more sources
COXETER COVERS OF THE CLASSICAL COXETER GROUPS [PDF]
International Journal of Algebra and Computation, 2010 Let C(T) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either Bn or Dn. Let CY(T) be a natural quotient of C(T), and if C(T) is simply-laced (which means all the relations between the generators has order 2 or 3), CY(T) is a generalized Coxeter group, too. Let At,n be a group which contains t Abelian
Meirav Amram +2 more
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The Sorting Order on a Coxeter Group [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Let $(W,S)$ be an arbitrary Coxeter system. For each sequence $\omega =(\omega_1,\omega_2,\ldots) \in S^{\ast}$ in the generators we define a partial order― called the $\omega \mathsf{-sorting order}$ ―on the set of group elements $W_{\omega} \subseteq W$
Drew Armstrong
doaj +6 more sources
Arithmetic of arithmetic Coxeter groups. [PDF]
Proc Natl Acad Sci U S A, 2019 Significance Conway’s topograph provided a combinatorial-geometric perspective on integer binary quadratic forms—quadratic functions of two variables with integer coefficients. This perspective is practical for solving equations and easily bounds the minima of binary quadratic forms.
Milea S, Shelley CD, Weissman MH.
europepmc +7 more sources
Discrete Mathematics & Theoretical Computer Science, 2004 Motivated by the Coxeter complex associated to a Coxeter system (W,S), we introduce a simplicial regular cell complex Δ(G,S) with a G-action associated to any pair (G,S) where G is a group and S is a finite set of generators for G which is ...
Eric Babson, Victor Reiner
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Shadows in Coxeter Groups [PDF]
Annals of Combinatorics, 2020 AbstractFor a givenwin a Coxeter groupW, the elementsusmaller thanwin Bruhat order can be seen as the end alcoves of stammering galleries of typewin the Coxeter complex$$\Sigma $$Σ. We generalize this notion and consider sets of end alcoves of galleries that are positively folded with respect to certain orientation$$\phi $$ϕof$$\Sigma $$Σ.
Graeber, Marius, Schwer, Petra
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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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Interval groups related to finite Coxeter groups Part II
Transactions of the London Mathematical Society, 2023 We provide a complete description of the presentations of the interval groups related to quasi‐Coxeter elements in finite Coxeter groups. In the simply laced cases, we show that each interval group is the quotient of the Artin group associated with the ...
Barbara Baumeister +3 more
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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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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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