## Abe, Takuro and Suyama, Daisuke and Tsujie, Shuhei - The freeness of Ish arrangements

dmtcs:2485 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
The freeness of Ish arrangements

Authors: Abe, Takuro and Suyama, Daisuke and Tsujie, Shuhei

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

Source : oai:HAL:hal-01337819v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: Hyperplane arrangement,Ish arrangement,Shi arrangement,Coxeter arrangement,Supersolvable arrangement,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]