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.
|ジャーナル||Discrete Mathematics and Theoretical Computer Science|
|出版ステータス||出版済み - 1 1 2015|
|イベント||27th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2015 - Daejeon, 大韓民国|
継続期間: 7 6 2015 → 7 10 2015
All Science Journal Classification (ASJC) codes
- コンピュータ サイエンス（全般）