Results 11 to 20 of about 2,366 (219)
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 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
Fairbairn, Ben
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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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Bender–Knuth Billiards in Coxeter Groups [PDF]
Forum of Mathematics, SigmaLet $(W,S)$ be a Coxeter system, and write $S=\{s_i:i\in I\}$ , where I is a finite index set. Fix a nonempty convex subset $\mathscr {L}$ of W. If W is of type A, then $\mathscr {L}$ is the set of linear extensions of a poset,
Grant Barkley +4 more
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On Subgroups of Coxeter Groups [PDF]
, 1998 A right-angled Coxeter group is a group with a given set of generators of order two, subject only to the relations that certain pairs of the generators commute. Various papers have shown how homological properties of the Coxeter group are related to homological properties of the simplicial complex whose simplices are the sets of commuting generators ...
Dicks, Warren, Leary, Ian J
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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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The facial weak order in finite Coxeter groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We investigate a poset structure that extends the weak order on a finite Coxeter group W to the set of all faces of the permutahedron of W. We call this order the facial weak order.
Aram Dermenjian +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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