Results 21 to 30 of about 3,228 (247)
Shi arrangements and low elements in Coxeter groups [PDF]
Proceedings of the London Mathematical Society, 2023 Given an arbitrary Coxeter system (W,S)$(W,S)$ and a non‐negative integer m$m$ , the m$m$ ‐Shi arrangement of (W,S)$(W,S)$ is a subarrangement of the Coxeter hyperplane arrangement of (W,S)$(W,S)$ .
M. Dyer +3 more
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Pop-stack-sorting for Coxeter groups [PDF]
Combinatorial Theory, 2021 Let $W$ be an irreducible Coxeter group. We define the Coxeter pop-stack-sorting operator $\mathsf{Pop}:W\to W$ to be the map that fixes the identity element and sends each nonidentity element $w$ to the meet of the elements covered by $w$ in the right ...
Colin Defant
semanticscholar +1 more source
On commensurable hyperbolic Coxeter groups
, 2016 For Coxeter groups acting non-cocompactly but with finite covolume on real hyperbolic space Hn, new methods are presented to distinguish them up to (wide) commensurability.
Rafael Guglielmetti +5 more
core +2 more sources
First-order aspects of Coxeter groups [PDF]
Journal of Algebra, 2020 We lay the foundations of the first-order model theory of Coxeter groups. Firstly, with the exception of the $2$-spherical non-affine case (which we leave open), we characterize the superstable Coxeter groups of finite rank, which we show to be ...
B. Mühlherr, G. Paolini, S. Shelah
semanticscholar +1 more source
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
doaj +2 more sources
Kazhdan-Lusztig polynomials of boolean elements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We give closed combinatorial product formulas for Kazhdan–Lusztig poynomials and their parabolic analogue of type $q$ in the case of boolean elements, introduced in [M. Marietti, Boolean elements in Kazhdan–Lusztig theory, J.
Pietro Mongelli
doaj +1 more source
The facial weak order in finite Coxeter groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We investigate a poset structure that extends the weak order on a finite Coxeter group W to the set of all faces of the permutahedron of W. We call this order the facial weak order.
Aram Dermenjian +2 more
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Word posets, with applications to Coxeter groups [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 We discuss the theory of certain partially ordered sets that capture the structure of commutation classes of words in monoids. As a first application, it follows readily that counting words in commutation classes is #P-complete.
Matthew J. Samuel
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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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Depth in Coxeter groups of type $B$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The depth statistic was defined for every Coxeter group in terms of factorizations of its elements into product of reflections. Essentially, the depth gives the minimal path cost in the Bruaht graph, where the edges have prescribed weights. We present an
Eli Bagno +2 more
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