Results 21 to 30 of about 342 (179)
Geometriae Dedicata, 2008 A solution of the isomorphism problem is presented for the class of Coxeter groups W that have a finite set of Coxeter generators S such that the underlying graph of the presentation diagram of the system (W,S) has the property that every cycle of length at least four has a cord.
Ratcliffe, John G., Tschantz, Steven T.
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Incoherent Coxeter Groups [PDF]
Proceedings of the American Mathematical Society, 2016 We use probabilistic methods to prove that many Coxeter groups are incoherent. In particular, this holds for Coxeter groups of uniform exponent > 2
Jankiewicz, Kasia, Wise, Daniel T.
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On a four-generator Coxeter group
International Journal of Mathematics and Mathematical Sciences, 2000 We study one of the 4-generator Coxeter groups and show that it is SQ-universal (SQU). We also study some other properties of the group.
Muhammad A. Albar
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International Journal of Algebra and Computation, 2020 Much is known about random right-angled Coxeter groups (i.e., right-angled Coxeter groups whose defining graphs are random graphs under the Erdös–Rényi model). In this paper, we extend this model to study random general Coxeter groups and give some results about random Coxeter groups, including some information about the homology of the nerve of a ...
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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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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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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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Coxeter groups as Beauville groups [PDF]
Monatshefte für Mathematik, 2015 We generalize earlier work of Fuertes and González-Diez as well as earlier work of Bauer, Catanese and Grunewald to Coxeter groups in general by classifying which of these are strongly real Beauville groups. As a consequence of this we determine which of these groups are Beauville groups. We also show that none of these groups are mixed Beaville groups
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Automorphisms of Coxeter groups [PDF]
Transactions of the American Mathematical Society, 2005 16 pages, no figures. Submitted to Trans. Amer.
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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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