Takuro Abe, Daisuke Suyama, Shuhei Tsujie
Published 2014-10-08Version 1
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.
A self-dual poset on objects counted by the Catalan numbers and a type-B analogue
The symmetry of the $(m,n)$-Rational $q, t$-Catalan numbers for $m=3$
A derivation of the Catalan numbers from a bijection between permutations and labeled trees
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