The freeness of Ish arrangements

Takuro Abe; Daisuke Suyama; Shuhei Tsujie

The freeness of Ish arrangements

Takuro Abe, Daisuke Suyama, Shuhei Tsujie

研究成果: ジャーナルへの寄稿 › 会議記事 › 査読

抄録

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.

本文言語	英語
ページ（範囲）	273-284
ページ数	12
ジャーナル	Discrete Mathematics and Theoretical Computer Science
出版ステータス	出版済み - 1月 1 2015
外部発表	はい
イベント	27th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2015 - Daejeon, 韓国継続期間: 7月 6 2015 → 7月 10 2015

!!!All Science Journal Classification (ASJC) codes

理論的コンピュータサイエンス
コンピュータサイエンス（全般）
離散数学と組合せ数学

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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.",

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N2 - 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.

AB - 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.

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Y2 - 6 July 2015 through 10 July 2015

ER -

The freeness of Ish arrangements

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!!!All Science Journal Classification (ASJC) codes

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