Takuro Abe ; Daisuke Suyama ; Shuhei Tsujie - 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) - https://doi.org/10.46298/dmtcs.2485
The freeness of Ish arrangementsConference paper

Authors: Takuro Abe 1; Daisuke Suyama ORCID2; Shuhei Tsujie ORCID2

  • 1 Department of Mechanical Engineering and Science
  • 2 Department of Mathematics [Sapporo]

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

https://doi.org/10.46298/dmtcs.2485
Source: 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
Imported 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]
Licence: Attribution 4.0 International (CC BY 4.0)

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