Results 81 to 90 of about 3,228 (247)
On excess in finite Coxeter groups [PDF]
Journal of Pure and Applied Algebra, 2015 For a finite Coxeter group $W$ and $w$ an element of $W$ the `excess' of $w$ is defined to be $e(w) = \min\{\ell(x) + \ell(y) - \ell(w) \; | \; w=xy, \; x^2 = y^2 = 1\}$ where $\ell$ is the length function on $W$. Here we investigate the behaviour of $e(w)$, and a related concept reflection excess, when restricted to standard parabolic subgroups of $W$.
Hart, Sarah B. +1 more
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Presentations of the braid group of the complex reflection group G(d,d,n)$G(d,d,n)$
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We show that the braid group associated to the complex reflection group G(d,d,n)$G(d,d,n)$ is an index d$d$ subgroup of the braid group of the orbifold quotient of the complex numbers by a cyclic group of order d$d$. We also give a compatible presentation of G(d,d,n)$G(d,d,n)$ and its braid group for each tagged triangulation of the disk with ...
Francesca Fedele, Bethany Rose Marsh
wiley +1 more source
An Eilenberg-Ganea phenomenon for actions with virtually cyclic stabilizers
, 2014 In dimension 3 and above, Bredon cohomology gives an acurate purely algebraic description of the minimal dimension of the classifying space for actions of a group with stabilisers in any given family of subgroups.
Martin G. Fluch +3 more
core +1 more source
Visual decompositions of Coxeter groups
Groups, Geometry, and Dynamics, 2009 A Coxeter system is an ordered pair (W,S) where S is the generating set in a particular type of presentation for the Coxeter group W. A subgroup of W is called special if it is generated by a subset of S. Amalgamated product decompositions of a Coxeter group having special factors and special amalgamated subgroup are easily recognized from the ...
Mihalik, Michael, Tschantz, Steven
openaire +3 more sources
Variants of a theorem of Macbeath in finite‐dimensional normed spaces
Mathematika, Volume 72, Issue 2, April 2026.Abstract A classical theorem of Macbeath states that for any integers d⩾2$d \geqslant 2$, n⩾d+1$n \geqslant d+1$, d$d$‐dimensional Euclidean balls are hardest to approximate, in terms of volume difference, by inscribed convex polytopes with n$n$ vertices.
Zsolt Lángi, Shanshan Wang
wiley +1 more source
Partial normalizations of coxeter arrangements and discriminants [PDF]
, 2012 We study natural partial normalization spaces of Coxeter arrangements and discriminants and relate their geometry to representation theory. The underlying ring structures arise from Dubrovin’s Frobenius manifold structure which is lifted (without unit)
Mond, D. (David) +3 more
core
Divergence of CAT(0) Cube Complexes and Coxeter Groups [PDF]
, 2016 We provide geometric conditions on a pair of hyperplanes of a CAT(0) cube complex that imply divergence bounds for the cube complex. As an application, we classify all right-angled Coxeter groups with quadratic divergence and show right-angled Coxeter ...
Ivan Levcovitz
semanticscholar +1 more source
On the Affine Weyl group of type A˜n−1
International Journal of Mathematics and Mathematical Sciences, 1987 We study in this paper the affine Weyl group of type A˜n−1, [1]. Coxeter [1] showed that this group is infinite. We see in Bourbaki [2] that A˜n−1 is a split extension of Sn, the symmetric group of degree n, by a group of translations and of lattice of ...
Muhammad A. Albar
doaj +1 more source
Coxeter Groups and Random Groups [PDF]
, 2019 For every dimension d, there is an infinite family of convex co-compact reflection groups of isometries of hyperbolic d-space --- the superideal (simplicial and cubical) reflection groups --- with the property that a random group at any density less than a half (or in the few relators model) contains quasiconvex subgroups commensurable with some member
openaire +2 more sources
, 2003 Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry. This largely self-contained work provides an intuitive and interdisciplinary treatment of Coxeter matroids, a new and beautiful generalization of ...
Borovik, Alexandre V +7 more
core +1 more source