Results 1 to 10 of about 252 (146)
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.
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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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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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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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Extending the weak order on Coxeter groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We introduce a new family of complete lattices, arising from a digraph together with a valuation on its vertices and generalizing a previous construction of the author.
Francois Viard
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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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Incoherent Coxeter Groups [PDF]
Proceedings of the American Mathematical Society, 2016 10 pages, 2 ...
Jankiewicz, Kasia, Wise, Daniel T.
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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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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
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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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