The freeness of Ish arrangements

Takuro Abe, Daisuke Suyama, Shuhei Tsujie

Research output: Contribution to journalConference articlepeer-review


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)273-284
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
Publication statusPublished - 2015
Externally publishedYes
Event27th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2015 - Daejeon, Korea, Republic of
Duration: Jul 6 2015Jul 10 2015

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science
  • Discrete Mathematics and Combinatorics


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