Results 11 to 20 of about 290 (179)
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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Journal of Algebra, 2011 We consider the class of those Coxeter groups for which removing from the Cayley graph any tubular neighbourhood of any wall leaves exactly two connected components. We call these Coxeter groups bipolar. They include both the virtually Poincare duality Coxeter groups and the infinite irreducible 2-spherical ones.
Caprace, Pierre-Emmanuel +1 more
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Spacelike Singularities and Hidden Symmetries of Gravity
Living Reviews in Relativity, 2008 We review the intimate connection between (super-)gravity close to a spacelike singularity (the “BKL-limit”) and the theory of Lorentzian Kac-Moody algebras.
Henneaux Marc +2 more
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Dimensionally Resolved Nanostructures of an Atomically Precise and Optically Active 1D van der Waals Helix. [PDF]
Adv MaterThe ability to grow nanostructures based on inorganic helical crystals with long‐range order will enable a platform to realize physical states that arise from chirality. Herein, it is demonstrated that controlled vapor phase deposition of an atomically precise helical crystal, GaSI, into ultrathin 1D nanowires and quasi‐2D nanoribbons.
Dold KG +15 more
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COXETER COVERS OF THE CLASSICAL COXETER GROUPS [PDF]
International Journal of Algebra and Computation, 2010 Let C(T) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either Bn or Dn. Let CY(T) be a natural quotient of C(T), and if C(T) is simply-laced (which means all the relations between the generators has order 2 or 3), CY(T) is a generalized Coxeter group, too. Let At,n be a group which contains t Abelian
Amram, Meirav +2 more
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Word posets, with applications to Coxeter groups [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 We discuss the theory of certain partially ordered sets that capture the structure of commutation classes of words in monoids. As a first application, it follows readily that counting words in commutation classes is #P-complete.
Matthew J. Samuel
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Depth in Coxeter groups of type $B$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The depth statistic was defined for every Coxeter group in terms of factorizations of its elements into product of reflections. Essentially, the depth gives the minimal path cost in the Bruaht graph, where the edges have prescribed weights. We present an
Eli Bagno +2 more
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A two-sided analogue of the Coxeter complex [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 For any Coxeter system (W, S) of rank n, we introduce an abstract boolean complex (simplicial poset) of dimension 2n − 1 which contains the Coxeter complex as a relative subcomplex.
T. Kyle Petersen
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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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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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