Results 11 to 20 of about 19,462 (147)
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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The freeness of Shi–Catalan arrangements [PDF]
European Journal of Combinatorics, 2011 12 ...
Takuro Abe, Hiroaki Terao
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The Shi arrangement of the type $D_{\ell}$
Proceedings of the Japan Academy Series A: Mathematical Sciences, 2012 In this paper, we give a basis for the derivation module of the cone over the Shi arrangement of the type $D_\ell$ explicitly.
Ruimei Gao, Hiroaki Terao
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Ad-nilpotent ideals and the Shi arrangement
Journal of Combinatorial Theory - Series A, 2013 We extend the Shi bijection from the Borel subalgebra case to parabolic subalgebras. In the process, the $I$-deleted Shi arrangement $\texttt{Shi}(I)$ naturally emerges. This arrangement interpolates between the Coxeter arrangement $\texttt{Cox}$ and the Shi arrangement $\texttt{Shi}$, and breaks the symmetry of $\texttt{Shi}$ in a certain symmetrical ...
Chao-Ping Dong
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A Survey of the Shi Arrangement
Association for Women in Mathematics Series, 2019 I would like to keep a running version on my website. If you know of work on the Shi arrangement that I have missed, please send me a tex summary and references.
Susanna Fishel, Fishel Susanna
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The braid and the Shi arrangements and the Pak–Stanley labelling [PDF]
European Journal of Combinatorics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rui Duarte, António Guedes de Oliveira
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Counting faces in the extended Shi arrangement
Advances in Applied Mathematics, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Richard Ehrenborg
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Shi arrangements and low elements in Coxeter groups [PDF]
Proceedings of the London Mathematical SocietyAbstractGiven an arbitrary Coxeter system and a non‐negative integer , the ‐Shi arrangement of is a subarrangement of the Coxeter hyperplane arrangement of . The classical Shi arrangement () was introduced in the case of affine Weyl groups by Shi to study Kazhdan–Lusztig cells for .
Dyer, Matthew +3 more
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Shi arrangements and low elements in affine Coxeter groups [PDF]
Canadian Journal of Mathematics, 2023 AbstractGiven an affine Coxeter group W, the corresponding Shi arrangement is a refinement of the corresponding Coxeter hyperplane arrangements that was introduced by Shi to study Kazhdan–Lusztig cells for W. Shi showed that each region of the Shi arrangement contains exactly one element of minimal length in W.
Chapelier-Laget, Nathan +1 more
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