Results 11 to 20 of about 177 (130)
Shi arrangements and low elements in Coxeter groups
Proceedings of the London Mathematical Society, Volume 129, Issue 2, August 2024.Abstract Given an arbitrary Coxeter system (W,S)$(W,S)$ and a non‐negative integer m$m$, the m$m$‐Shi arrangement of (W,S)$(W,S)$ is a subarrangement of the Coxeter hyperplane arrangement of (W,S)$(W,S)$. The classical Shi arrangement (m=0$m=0$) was introduced in the case of affine Weyl groups by Shi to study Kazhdan–Lusztig cells for W$W$.
Matthew Dyer +3 more
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Partial Normalizations of Coxeter Arrangements and Discriminants [PDF]
Moscow Mathematical Journal, 2012 24 pages, 1 figure, amended ...
Granger, Michel +2 more
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Basic Derivations for Subarrangements of Coxeter Arrangements [PDF]
Journal of Algebraic Combinatorics, 1993 Let \({\mathfrak A}\), \({\mathfrak B}\), \({\mathfrak D}\) denote the families of arrangements associated with the root systems of types \(A\), \(B\), \(D\). Then \({\mathfrak A}_{n-1}\subset{\mathfrak D}_ n\subset {\mathfrak B}_ n\). The authors determine the freeness of certain families of arrangements interpolating between these reflection ...
Józefiak, Tadeusz, Sagan, Bruce E.
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Cohomology of Coxeter arrangements and Solomon’s descent algebra [PDF]
Transactions of the American Mathematical Society, 2014 We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group W W ...
Douglass, J. Matthew +2 more
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An inductive approach to Coxeter arrangements and Solomon’s descent algebra [PDF]
Journal of Algebraic Combinatorics, 2011 21 pages; to appear in J.
Dolan, J. Matthew +2 more
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On the invariants of the cohomology of complements of Coxeter arrangements
Journal of Algebra, 2020 We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group W. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the space of W-invariants in this cohomology ring.
J. Matthew Douglass +2 more
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Periodic arrangements of tetrahedra having appearances similar to that of the Boerdijk-Coxeter helix. [PDF]
Sci RepThe Boerdijk-Coxeter helix (BC helix or tetrahelix) is a linear stacking of regular tetrahedra. Although the BC helix exhibits an aperiodic nature, structures resembling the BC helix with periodicity are found in materials. To understand such structures, we considered a modification of the BC helix to introduce periodicity.
Onaka S.
europepmc +4 more sources
The double Coxeter arrangement
Commentarii Mathematici Helvetici, 1998 Consider a finite collection \(\mathcal A\) of linear hyperplanes in \({\mathbb R}^\ell\). Let \(\alpha_H: {\mathbb R}^\ell \to {\mathbb R}\) satisfy \(H=\ker \alpha_H\), for \(H\in {\mathcal A}\). Let \(S={\mathbb R}[x_1,\ldots,x_\ell]\). A derivation \(\theta\) of \(S\) is tangent along \(\mathcal A\) if \(\theta(\alpha_H)\) is a multiple of ...
Solomon, L., Terao, H.
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On Coxeter Arrangements and the Coxeter Number
Advanced Studies in Pure Mathematics, 2018 Let $(G, V)$ be an irreducible Coxeter group and let $\mathscr{A}$ be the corresponding Coxeter arrangement. Let $H \in \mathscr{A}$ be a hyperplane and let $\mathscr{A}^H$ be the restriction of $\mathscr{A}$ to $H$. Let $h$ be the Coxeter number. We prove that \[|\mathscr{A}^H|=|\mathscr{A}|-h+1\] and show that $\mathscr{A}^H$ is a free arrangement ...
Orlik, Peter +2 more
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Morphisms and Order Ideals of Toric Posets
Mathematics, 2016 Toric posets are in some sense a natural “cyclic” version of finite posets in that they capture the fundamental features of a partial order but without the notion of minimal or maximal elements.
Matthew Macauley
doaj +1 more source