Results 11 to 20 of about 2,142 (221)
International Journal of Mathematics and Mathematical Sciences, 2000 We show that the Coxeter group Dn is the split extension of n−1 copies of Z2 by Sn for a given action of Sn described in the paper. We also find the centre of Dn and some of its other important subgroups.
M. A. Albar, Norah Al-Saleh
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On a four-generator Coxeter group [PDF]
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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Symmetric presentations of Coxeter groups [PDF]
Proceedings of the Edinburgh Mathematical Society, 2011 AbstractWe apply the techniques of symmetric generation to establish the standard presentations of the finite simply laced irreducible finite Coxeter groups, that is, the Coxeter groups of typesAn,DnandEn, and show that these are naturally arrived at purely through consideration of certain natural actions of symmetric groups.
Fairbairn, Ben, Ben Fairbairn
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Coxeter's enumeration of Coxeter groups
Journal of the London Mathematical SocietyAbstract In a short paper that appeared in the Journal of the London Mathematical Society in 1934, H. S. M. Coxeter completed the classification of finite Coxeter groups.
Bernhard Mühlherr, Richard M. Weiss
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Coxeter quotients of the automorphism group of a Coxeter group
, 2020 We show that for a large class $\mathcal{W}$ of Coxeter groups the following holds: Given a group $W_Γ$ in $\mathcal{W}$, the automorphism group ${\rm Aut}(W_Γ)$ virtually surjects onto some infinite Coxeter group. In particular, the group ${\rm Aut}(W_Γ)$ is virtually indicable and therefore does not have Kazhdan's property (T).
Varghese, Olga
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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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Brain Morphology in Extraordinary Geometrician Harold Coxeter: implications for connectivity [PDF]
Alzheimers DementAbstract Background While extensive research has examined brain‐behavior relationships in cognitive decline, far less study of the other extreme has been done with super‐agers or those with extraordinary abilities. Harold Coxeter (HC), an extraordinary geometrician (Figure 1), considered one of the foremost mathematical minds of the 20th century ...
Scott C +7 more
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Kazhdan-Lusztig polynomials of boolean elements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We give closed combinatorial product formulas for Kazhdan–Lusztig poynomials and their parabolic analogue of type $q$ in the case of boolean elements, introduced in [M. Marietti, Boolean elements in Kazhdan–Lusztig theory, J.
Pietro Mongelli
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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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k-Parabolic Subspace Arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 In this paper, we study k-parabolic arrangements, a generalization of the k-equal arrangement for any finite real reflection group. When k=2, these arrangements correspond to the well-studied Coxeter arrangements.
Christopher Severs, Jacob White
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