Results 31 to 40 of about 1,721 (200)
Schubert varieties, inversion arrangements, and Peterson translation [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We show that an element $\mathcal{w}$ of a finite Weyl group W is rationally smooth if and only if the hyperplane arrangement $\mathcal{I} (\mathcal{w})$ associated to the inversion set of \mathcal{w} is inductively free, and the product $(d_1+1) ...(d_l+
William Slofstra
doaj +1 more source
Logarithmic Discriminants of Hyperplane Arrangements [PDF]
Le Matematiche20 pages, comments welcome!
L. Kayser, A. Kretschmer, S. Telen
openaire +5 more sources
Branched Polymers and Hyperplane Arrangements [PDF]
Discrete & Computational Geometry, 2013 We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie, and Kenyon and Winkler to any hyperplane arrangement A. The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A is ...
Postnikov, Alexander, Meszaros, Karola
openaire +5 more sources
A computation on the decomposition factors of D -modules over a hyperplane arrangement in space [PDF]
, 2020 Let m be a positive integer,α_i:C^n⟶C^n, for i=1,2,…,m be linear forms and H_i={P∈C^n:α_i (P)=0} be the corresponding hyperplane for each i=1,2,…,m . The linear forms α_1,α_2,…,α_m define a hyperplane arrangement and X=C^n\V(α), where α=∏_(i=1)^m α_i and
Ababaw, Tilahun, Demelash, Smegnsh
core +2 more sources
The Shi arrangement and the Ish arrangement [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 This paper is about two arrangements of hyperplanes. The first — the Shi arrangement — was introduced by Jian-Yi Shi to describe the Kazhdan-Lusztig cells in the affine Weyl group of type A.
Drew Armstrong, Brendon Rhoades
doaj +1 more source
Geometric aspects of the Jacobian of a hyperplane arrangement [PDF]
, 2023 An embedding of the complete bipartite graph $K_{3,3}$ in $\mathbb{P}^2$ gives rise to both a line arrangement and a bar-and-joint framework. For a generic placement of the six vertices, the graded Betti numbers of the logarithmic module of derivations ...
Sidman, Jessica +2 more
core +1 more source
Poset topology and homological invariants of algebras arising in algebraic combinatorics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We present a beautiful interplay between combinatorial topology and homological algebra for a class of monoids that arise naturally in algebraic combinatorics. We explore several applications of this interplay.
Stuart Margolis +2 more
doaj +1 more source
Arrangements of oriented hyperplanes [PDF]
Discrete & Computational Geometry, 1993 The paper refers to arrangements of \(n\) oriented hyperplanes in \(E^ d\). For \(n\) and \(d\) given, the author derives an upper bound on the number \(c_ k\) of convex cells which are covered by precisley \(k\) half-spaces. Denoting the corresponding maximal number by \(C_ k(n,d)\), for \(n>d\) the following recursive inequality holds: \[ C_ k(n,d ...
openaire +1 more source
Face monoid actions and tropical hyperplane arrangements [PDF]
, 2017 We study the combinatorics of tropical hyperplane arrangements, and their relationship to (classical) hyperplane face monoids. We show that the refinement operation on the faces of a tropical hyperplane arrangement, introduced by Ardila and Develin in ...
Kambites, Mark +3 more
core +1 more source
The module of affine descents [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 The goal of this paper is to introduce an algebraic structure on the space spanned by affine descent classes of a Weyl group, by analogy and in relation to the structure carried by ordinary descent classes.
Marcelo Aguiar, Kile T. Petersen
doaj +1 more source