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Free Subarrangements of Shi Arrangements
Graphs and Combinatorics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zixuan Wang, Guangfeng Jiang
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On the Falk Invariant of Shi and Linial Arrangements [PDF]
Discrete and Computational Geometry, 2021 It is an open question to give a combinatorial interpretation of the Falk invariant of a hyperplane arrangement, i.e. the third rank of successive quotients in the lower central series of the fundamental group of the arrangement. In this article, we give a combinatorial formula for this invariant in the case of hyperplane arrangements that are complete
Weili Guo, Michele Torielli
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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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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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Some new result on Shi arrangement
AIP Conference Proceedings, 2023Alaa Abdulhaleem Abdulah +1 more
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Geometriae Dedicata, 2003
An arrangement of hyperplanes \(\mathcal H\) in real affine space divides the affine space into open cells referred to as the faces of \(\mathcal H\). Well-known formulae express the number of faces of each dimension. When considering the complex complement arrangement, these numbers have a cohomological interpretation.
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An arrangement of hyperplanes \(\mathcal H\) in real affine space divides the affine space into open cells referred to as the faces of \(\mathcal H\). Well-known formulae express the number of faces of each dimension. When considering the complex complement arrangement, these numbers have a cohomological interpretation.
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