Results 21 to 30 of about 2,366 (219)
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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Cyclically reduced elements in Coxeter groups [PDF]
, 2020 Let W be a Coxeter group. We provide a precise description of the conjugacy classes in W, in the spirit of Matsumoto's theorem. This extends to all Coxeter groups an important result on finite Coxeter groups by M. Geck and G. Pfeiffer from 1993.
Marquis, Timothée
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Involution products in Coxeter groups [PDF]
, 2011 For W a Coxeter group, let = {w ∈ W | w = xy where x, y ∈ W and x 2 = 1 = y 2}. It is well known that if W is finite then W = . Suppose that w ∈ . Then the minimum value of ℓ(x) + ℓ(y) – ℓ(w), where x, y ∈ W with w = xy and x 2 = 1 = y 2, is called
P. J. Rowley +6 more
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Coxeter groups and the PMNS matrix
European Physical Journal C: Particles and Fields, 2017 We discuss symmetries of the Lagrangian of the leptonic sector. We consider the case when this symmetry group is a Coxeter group, and identify the low energy residual symmetries with the involution generators, i.e., generators with order equal to 2.
Pritibhajan Byakti, Palash B. Pal
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IRREDUCIBLE COXETER GROUPS [PDF]
International Journal of Algebra and Computation, 2007 We prove that a non-spherical irreducible Coxeter group is (directly) indecomposable and that an indefinite irreducible Coxeter group is strongly indecomposable in the sense that all its finite index subgroups are (directly) indecomposable. Let W be a Coxeter group.
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Equivariant K-homology for some Coxeter groups [PDF]
, 2007 We obtain the equivariant K-homology of the classifying space \underline{E}W for W a right-angled or, more generally, an even Coxeter group. The key result is a formula for the relative Bredon homology of \underline{E}W in terms of Coxeter cells.
Sanchez-Garcia, Ruben
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Fully commutative elements and lattice walks [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 An element of a Coxeter group $W$ is fully commutative if any two of its reduced decompositions are related by a series of transpositions of adjacent commuting generators. These elements were extensively studied by Stembridge in the finite case.
Riccardo Biagioli +2 more
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Hereditary conjugacy separability of right angled Artin groups and its applications [PDF]
, 2012 We prove that finite index subgroups of right angled Artin groups are conjugacy separable. We then apply this result to establish various properties of other classes of groups.
Minasyan, Ashot
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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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