The Shi arrangement and the Ish arrangement

DOI10.1090/S0002-9947-2011-05521-2zbMath1238.05271arXiv1009.1655MaRDI QIDQ2880689

Drew Armstrong, Brendon Rhoades

Publication date: 13 April 2012

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.1655

Mathematics Subject Classification ID

Related Items (17)

Partial parking functions ⋮ Bigraphical arrangements ⋮ The freeness of Ish arrangements ⋮ Deformations of the braid arrangement and trees ⋮ Bijections for faces of the Shi and Catalan arrangements ⋮ Ad-nilpotent ideals and the Shi arrangement ⋮ Between Shi and Ish ⋮ The number of parking functions with center of a given length ⋮ Eulerian polynomials for subarrangements of Weyl arrangements ⋮ On \({\boldsymbol q}\)-Counting of Noncrossing Chains and Parking Functions ⋮ Vertex-weighted digraphs and freeness of arrangements between Shi and Ish ⋮ Bijections for the Shi and Ish arrangements ⋮ Parking spaces. ⋮ The Bernardi formula for nontransitive deformations of the braid arrangement ⋮ Hyperplane arrangements between Shi and Ish ⋮ Affine permutations and rational slope parking functions ⋮ Free subarrangements of Shi arrangements

Cites Work

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• Enumeration of connected Catalan objects by type
• The Kazhdan-Lusztig cells in certain affine Weyl groups
• On geometric semilattices
• A simple bijection for the regions of the Shi arrangement of hyperplanes
• On a family of hyperplane arrangements related to the affine Weyl groups
• On free deformations of the braid arrangement
• Deformations of Coxeter hyperplane arrangements
• Sur les partitions non croisées d'un cycle. (The non-crossed partitions of a cycle)
• Characteristic polynomials of subspace arrangements and finite fields
• Facing up to arrangements: face-count formulas for partitions of space by hyperplanes
• On the Foundations of Combinatorial Theory II. Combinatorial Geometries

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