The freeness of Ish arrangements

Takuro Abe, Daisuke Suyama, Shuhei Tsujie

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The Ish arrangement was introduced by Armstrong to give a new interpretation of the q,t-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish arrangement and posed some problems. One of them is whether the Ish arrangement is a free arrangement or not. In this paper, we verify that the Ish arrangement is supersolvable and hence free. Moreover, we give a necessary and sufficient condition for the deleted Ish arrangement to be free.

Original languageEnglish
Pages (from-to)169-183
Number of pages15
JournalJournal of Combinatorial Theory. Series A
Volume146
DOIs
Publication statusPublished - Feb 1 2017

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Necessary Conditions
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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

The freeness of Ish arrangements. / Abe, Takuro; Suyama, Daisuke; Tsujie, Shuhei.

In: Journal of Combinatorial Theory. Series A, Vol. 146, 01.02.2017, p. 169-183.

Research output: Contribution to journalArticle

Abe, Takuro ; Suyama, Daisuke ; Tsujie, Shuhei. / The freeness of Ish arrangements. In: Journal of Combinatorial Theory. Series A. 2017 ; Vol. 146. pp. 169-183.
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