Results 21 to 30 of about 23,334 (203)
Coxeter group in Hilbert geometry [PDF]
, 2015 A theorem of Tits - Vinberg allows to build an action of a Coxeter group $\Gamma$ on a properly convex open set $\Omega$ of the real projective space, thanks to the data $P$ of a polytope and reflection across its facets.
Marquis, Ludovic
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Asymptotical behaviour of roots of infinite Coxeter groups I [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Let $W$ be an infinite Coxeter group, and $\Phi$ be the root system constructed from its geometric representation. We study the set $E$ of limit points of "normalized'' roots (representing the directions of the roots).
Christophe Hohlweg +2 more
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Shortest path poset of finite Coxeter groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We define a poset using the shortest paths in the Bruhat graph of a finite Coxeter group $W$ from the identity to the longest word in $W, w_0$. We show that this poset is the union of Boolean posets of rank absolute length of $w_0$; that is, any shortest
Saúl A. Blanco
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Non-orthogonal geometric realizations of Coxeter groups [PDF]
, 2012 We define in an axiomatic fashion a \emph{Coxeter datum} for an arbitrary Coxeter group $W$. This Coxeter datum will specify a pair of reflection representations of $W$ in two vector spaces linked only by a bilinear paring without any integrality and non-
Bourbaki +6 more
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FCC, BCC and SC Lattices Derived from the Coxeter-Weyl groups and quaternions
Sultan Qaboos University Journal for Science, 2014 We construct the fcc (face centered cubic), bcc (body centered cubic) and sc (simple cubic) lattices as the root and the weight lattices of the affine extended Coxeter groups W(A3) and W(B3)=Aut(A3).
Nazife Özdeş Koca +2 more
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Garside families in Artin-Tits monoids and low elements in Coxeter groups [PDF]
, 2014 We show that every finitely generated Artin-Tits group admits a finite Garside family, by introducing the notion of a low element in a Coxeter group and proving that the family of all low elements in a Coxeter system (W, S) with S finite includes S and ...
Dehornoy, Patrick +2 more
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On the Affine Weyl group of type A˜n−1
International Journal of Mathematics and Mathematical Sciences, 1987 We study in this paper the affine Weyl group of type A˜n−1, [1]. Coxeter [1] showed that this group is infinite. We see in Bourbaki [2] that A˜n−1 is a split extension of Sn, the symmetric group of degree n, by a group of translations and of lattice of ...
Muhammad A. Albar
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Projection of Polyhedra onto Coxeter Planes Described with Quaternions
Sultan Qaboos University Journal for Science, 2015 3-dimensional convex uniform polyhedra have been projected onto their corresponding Coxeter planes defined by the simple roots of the Coxeter diagram ,
Mudhahir Al-Ajmi +2 more
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An algorithm for an 𝓁2-homological test for the planarity of a graph
AKCE International Journal of Graphs and Combinatorics, 2020 Given a finite simple graph Γ, one is able to define the presentation of an associate Coxeter group and construct a CW-complex on which the associated Coxeter group acts.
Elizabeth Donovan, Timothy Schroeder
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Completely positive maps for imprimitive complex reflection groups
Karpatsʹkì Matematičnì Publìkacìï, 2021 In 1994, M. Bożejko and R. Speicher proved the existence of completely positive quasimultiplicative maps from the group algebra of Coxeter groups to the set of bounded operators.
H. Randriamaro
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