The freeness of Ish arrangements
Combinatorics
2018-05-25 v3
Abstract
The Ish arrangement was introduced by Armstrong to give a new interpretation of the -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.
Keywords
Cite
@article{arxiv.1410.2084,
title = {The freeness of Ish arrangements},
author = {Takuro Abe and Daisuke Suyama and Shuhei Tsujie},
journal= {arXiv preprint arXiv:1410.2084},
year = {2018}
}
Comments
We added Section 3 (v2). We corrected the proof of Theorem 1.3 and several typos (v3)