Results 1 to 10 of about 177 (130)
Hyperfactord of Shi arrangement Sh(A2) and Sh(A3)
Al-Mustansiriyah Journal of Science, 2022 In this paper, we introduce the region and the faces poset of shi arrangement that J. Y. Shi firstly introduced it. This is an affine arrangement, each of whose hyperplane is parallel to some"hyperplane of Coxeter arrangement"(Braid arrangement), the ...
Alaa A. A. Al-Mujmaey +1 more
doaj +1 more source
k-Parabolic Subspace Arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 In this paper, we study k-parabolic arrangements, a generalization of the k-equal arrangement for any finite real reflection group. When k=2, these arrangements correspond to the well-studied Coxeter arrangements.
Christopher Severs, Jacob White
doaj +1 more source
Gallery Posets of Supersolvable Arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for the longest element whose Hasse diagram is the graph of ...
Thomas McConville
doaj +1 more source
The freeness of Ish arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The Ish arrangement was introduced by Armstrong to give a new interpretation of the $q; t$-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish arrangement ...
Takuro Abe +2 more
doaj +1 more source
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
doaj +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
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
wiley +1 more source
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
wiley +1 more source
Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors
Proceedings of the London Mathematical Society, Volume 127, Issue 3, Page 513-588, September 2023., 2023 Abstract We show that the mesh mutations are the minimal relations among the g${\bm{g}}$‐vectors with respect to any initial seed in any finite‐type cluster algebra. We then use this algebraic result to derive geometric properties of the g${\bm{g}}$‐vector fan: we show that the space of all its polytopal realizations is a simplicial cone, and we then ...
Arnau Padrol +3 more
wiley +1 more source
Gaudin algebras, RSK and Calogero–Moser cells in Type A
Proceedings of the London Mathematical Society, Volume 126, Issue 5, Page 1467-1495, May 2023., 2023 Abstract We study the spectrum of a family of algebras, the inhomogeneous Gaudin algebras, acting on the n$n$‐fold tensor representation C[x1,…,xr]⊗n${\mathbb{C}}[x_1, \ldots , x_r]^{\otimes n}$ of the Lie algebra glr$\mathfrak {gl}_r$. We use the work of Halacheva–Kamnitzer–Rybnikov–Weekes to demonstrate that the Robinson–Schensted–Knuth ...
Adrien Brochier, Iain Gordon, Noah White
wiley +1 more source