The freeness of Shi-Catalan arrangements

Takuro Abe, Hiroaki Terao

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let W be a finite Weyl group and A be the corresponding Weyl arrangement. A deformation of A is an affine arrangement which is obtained by adding to each hyperplane H∈A several parallel translations of H by the positive root (and its integer multiples) perpendicular to H. We say that a deformation is W-equivariant if the number of parallel hyperplanes of each hyperplane H∈A depends only on the W-orbit of H. We prove that the conings of the W-equivariant deformations are free arrangements under a Shi-Catalan condition and give a formula for the number of chambers. This generalizes Yoshinaga's theorem conjectured by Edelman-Reiner.

Original languageEnglish
Pages (from-to)1191-1198
Number of pages8
JournalEuropean Journal of Combinatorics
Volume32
Issue number8
DOIs
Publication statusPublished - Nov 1 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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