The freeness of Ish arrangements

Takuro Abe, Daisuke Suyama, Shuhei Tsujie

Research output: Contribution to journalArticle

2 Citations (Scopus)


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
Publication statusPublished - Feb 1 2017


All Science Journal Classification (ASJC) codes

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

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