Results 21 to 30 of about 15,709 (204)
A complex for right-angled Coxeter groups [PDF]
Proceedings of the American Mathematical Society, 2002 Given a finite graph \(\Gamma\), the graph group, or right angled Artin group \(A\Gamma\), is generated by the vertex set of \(\Gamma\) and the relations are precisely the commutators between pairs of vertices joined by an edge of \(\Gamma\). Let \(N\) be the normal closure of the set of squares of the generators of \(A\Gamma\).
Carl Droms
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An Explicit Description of Coxeter Homology Complexes [PDF]
ISRN Geometry, 2011 Rains (2010) computes the integral homology of real De Concini-Procesi models of subspace arrangements, using some homology complexes whose main ingredients are nested sets and building sets of subspaces. We think that it is useful to provide various different descriptions of these complexes, since they encode relevant information about the homotopy ...
Filippo Callegaro, Giovanni Gaiffi
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Convex Geometry of Subword Complexes of Coxeter Groups
, 2020 Diese Monographie präsentiert Ergebnisse im Zusammenhang mit einer Familie von simplizialen Komplexen, die "Subwortkomplexe" genannt werden. Diese Simplizialkomplexe werden mit Hilfe der Bruhat-Ordnung von Coxeter-Gruppen definiert. Trotz einer einfachen kombinatorischen Definition werden viele ihrer kombinatorischen Eigenschaften immer noch nicht ...
Jean‐Philippe Labbé
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On Coxeter diagrams of complex reflection groups [PDF]
Transactions of the American Mathematical Society, 2012 We study Coxeter diagrams of some unitary reflection groups. Using solely the combinatorics of diagrams, we give a new proof of the classification of root lattices defined over $\cE = \ZZ[e^{2 i/3}]$: there are only four such lattices, namely, the $\cE$-lattices whose real forms are $A_2$, $D_4$, $E_6$ and $E_8$.
Tathagata Basak
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Homotopy Type of the Boolean Complex of a Coxeter System [PDF]
Advances in Mathematics, 2008 In any Coxeter group, the set of elements whose principal order ideals are boolean forms a simplicial poset under the Bruhat order. This simplicial poset defines a cell complex, called the boolean complex. In this paper it is shown that, for any Coxeter system of rank n, the boolean complex is homotopy equivalent to a wedge of (n-1)-dimensional spheres.
Kári Ragnarsson, Bridget Eileen Tenner
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Decomposition of Polyharmonic Functions with Respect to the Complex Dunkl Laplacian
Journal of Inequalities and Applications, 2010 Let Ω be a G-invariant convex domain in ℂN including 0, where G is a complex Coxeter group associated with reduced root system R⊂ℝN. We consider holomorphic functions f defined in Ω which are Dunkl polyharmonic, that
Guangbin Ren, Helmuth R. Malonek
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Shadows in Coxeter groups [PDF]
, 2020 For a given $w$ in a Coxeter group $W$ the elements $u$ smaller than $w$ in Bruhat order can be seen as the end-alcoves of stammering galleries of type $w$ in the Coxeter complex $\Sigma$.
Graeber, Marius, Schwer, Petra
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Discrete Mathematics & Theoretical Computer Science, 2012 We present a family of simplicial complexes called \emphmulti-cluster complexes. These complexes generalize the concept of cluster complexes, and extend the notion of multi-associahedra of types ${A}$ and ${B}$ to general finite Coxeter groups.
Cesar Ceballos +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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FRIEZE PATTERNS WITH COEFFICIENTS
Forum of Mathematics, Sigma, 2020 Frieze patterns, as introduced by Coxeter in the 1970s, are closely related to cluster algebras without coefficients. A suitable generalization of frieze patterns, linked to cluster algebras with coefficients, has only briefly appeared in an unpublished ...
MICHAEL CUNTZ +2 more
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