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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
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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
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Hyperplane arrangements between Shi and Ish [PDF]
Electronic Notes in Discrete Mathematics, 2018 Abstract We introduce a new family of hyperplane arrangements in dimension n ≥ 3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of this family have the same number of regions — the connected components of the complement of the union of the hyperplanes — which can be bijectively labeled with the ...
Rui Duarte, Antonio Guedes De Oliveira
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Vertex-weighted digraphs and freeness of arrangements between Shi and Ish
European Journal of Combinatorics, 2021 We introduce and study a digraph analogue of Stanley's $ψ$-graphical arrangements from the perspectives of combinatorics and freeness. Our arrangements form a common generalization of various classes of arrangements in literature including the Catalan arrangement, the Shi arrangement, the Ish arrangement, and especially the arrangements interpolating ...
Takuro Abe +2 more
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Hyperplane Arrangements and Diagonal Harmonics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 In 2003, Haglund's bounce statistic gave the first combinatorial interpretation of the q,t-Catalan numbers and the Hilbert series of diagonal harmonics. In this paper we propose a new combinatorial interpretation in terms of the affine Weyl group of type
Drew Armstrong
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Journal of Marine Science and Engineering, 2023 This paper investigates the hydroelastic responses of offshore floating solar photovoltaic farms (OFPVs). OFPVs usually occupy a large sea space in the order of hectares and structural deformation under wave action has to be taken into consideration due ...
Zhi Yung Tay
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Compiling a Dictionary of an Unwritten Language: A Non-corpus-based Approach
Lexikos, 2011 <p>Abstract: In this article an account is given of the experience in fieldwork by the Dictionary of the Flemish Dialects (Woordenboek van de Vlaamse Dialecten, WVD), Ghent University, Belgium.
Jacques van Keymeulen
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Defining the role of NG2-expressing cells in experimental models of multiple sclerosis. A biofunctional analysis of the neurovascular unit in wild type and NG2 null mice. [PDF]
PLoS ONE, 2019 During experimental autoimmune encephalomyelitis (EAE), a model for multiple sclerosis associated with blood-brain barrier (BBB) disruption, oligodendrocyte precursor cells (OPCs) overexpress proteoglycan nerve/glial antigen 2 (NG2), proliferate, and ...
Francesco Girolamo +10 more
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A type $B$ analog of Ish arrangement
, 2023 The Shi arrangement due to Shi (1986) and the Ish arrangement due to Armstrong (2013) are deformations of the type $A$ Coxeter arrangement that share many common properties. Motivated by a question of Armstrong and Rhoades since 2012 to seek for Ish arrangements of other types, in this paper we introduce an Ish arrangement of type $B$.
Tran, Tan Nhat, Tsujie, Shuhei
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Bijections for the Shi and Ish arrangements
European Journal of Combinatorics, 2014 The {\sf Shi hyperplane arrangement} Shi(n) was introduced by Shi to study the Kazhdan-Lusztig cellular structure of the affine symmetric group. The {\sf Ish hyperplane arrangement} Ish(n) was introduced by Armstrong in the study of diagonal harmonics. Armstrong and Rhoades discovered a deep combinatorial similarity between the Shi and Ish arrangements.
Emily Leven +2 more
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