Results 1 to 10 of about 19,463 (248)
A simple bijection for the regions of the Shi arrangement of hyperplanes
Discrete Mathematics, 1999 The Shi arrangement Ln is the arrangement of affine hyperplanes in Rn of the form xi − xj = 0 or 1, for 1 ⩽ i < j ⩽ n. It dissects Rn into (n + 1)n−1 regions, as was first proved by Shi. We give a simple bijective proof of this result.
Christos A Athanasiadis +1 more
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Hyperplane arrangements between Shi and Ish [PDF]
Electronic Notes in Discrete Mathematics, 2018 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 ...
Rui Duarte, Antonio Guedes De Oliveira
exaly +5 more sources
Freeness for restriction arrangements of the extended Shi and Catalan arrangements
Discrete Mathematics, 2023 The extended Shi and Catalan arrangements are well investigated arrangements. In this paper, we prove that the cone of the extended Catalan arrangement of type A is always hereditarily free, while we determine the dimension in which the cone of the ...
Norihiro Nakashima, Shuhei Tsujie
exaly +5 more sources
On the two variable distance enumerator of the Shi hyperplane arrangement
European Journal of Combinatorics, 2008 We give an interpretation for the coefficients of the two variable refinement DSn(q,t) of the distance enumerator of the Shi hyperplane arrangement Sn in n dimensions. This two variable refinement was defined by Stanley in [R.P.
Sivaramakrishnan Sivasubramanian
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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
doaj +2 more sources
A Class of Labeled Posets and the Shi Arrangement of Hyperplanes
Journal of Combinatorial Theory - Series A, 1997 We consider the class Pnof labeled posets onnelements which avoid certain three-element induced subposets. We show that the number of posets in Pnis (n+1)n−1by exploiting a bijection between Pnand the set of regions of the arrangement of hyperplanes in ...
Christos A Athanasiadis
exaly +4 more sources
Bijections of dominant regions in the $m$-Shi arrangements of type $A$, $B$ and $C$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 In the present paper, the relation between the dominant regions in the $m$-Shi arrangement of types $B_n/C_n$, and those of the $m$-Shi arrangement of type $A_{n-1}$ is investigated. More precisely, it is shown explicitly how the sets $R^m(B_n)$ and $R^m(
Myrto Kallipoliti, Eleni Tzanaki
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Counting Shi regions with a fixed separating wall [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant ...
Susanna Fishel +2 more
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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
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Commentary on the Song Dynasty Incomplete Block-printed Edition of the Men Lei Zeng Guang Shi Zhu Du Gong Bu Shi in the National Library of China [PDF]
Journal of Library and Information Studies, 2022 The Men Lei Zeng Guang Shi Zhu Du Gong Bu Shi (門類增廣十注杜工部詩) collected by National Library of China, is one of the rare surviving editions of Song dynasty.
Qi-Xiu Zhang, Wei Sun
doaj +1 more source