Results 21 to 30 of about 304 (161)
Characteristic Quasi-polynomials for Deformations of Coxeter Arrangements of Types A, B, C, and D
Order34 ...
Yusuke Mori 0005, Norihiro Nakashima
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Bases for modules of differential operators [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 It is well-known that the derivation modules of Coxeter arrangements are free. Holm began to study the freeness of modules of differential operators on hyperplane arrangements. In this paper, we study the cases of the Coxter arrangements of type A, B and
Norihiro Nakashima
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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
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The double coxeter arrangement
The double coxeter arrangementLet V be Euclidean space. Let WC GL(V) be a finite irreducible reflection group. Let A be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H E A choose O'.H E V* such that H = ker( O'.H ). The arrangement A is known to be free: the derivation module D(A) = {8 E Ders I 8(aH) E SaH} is a free S-module with ...
Solomon, L., Terao, H.
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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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SusMat, Volume 3, Issue 6, Page 781-820, December 2023., 2023 Electrocatalytic C─N coupling using CO2 and biomass as carbon sources holds great promise for the synthesis of organic nitrogen compounds. This review summarizes the recent research progress in electrocatalytic C─N coupling, mainly focusing on material design and working mechanisms.
Hao Jiang +6 more
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Enantiomeric discrimination by chiral electromagnetic resonance enhancement
Chirality, Volume 35, Issue 10, Page 732-738, October 2023., 2023 The origin of enantiomeric discrimination arising because of the interaction between gold tetrahelices and molecules with helical chirality is explained based on scattered field enhancement. Weakly scattering chiral molecules are detectable in the near vicinity of gold tetrahelices upon illumination by a plane polarized electromagnetic wave.
Prashant Kumar +2 more
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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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