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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.
We introduce and study a digraph analogue of Stanleys $psi$-graphical arrangements from the perspectives of combinatorics and freeness. Our arrangements form a common generalization of various classes of arrangements in literature including the Catal
Let $W$ be a finite Weyl group and $A$ be the corresponding Weyl arrangement. A deformation of $A$ is an affine arrangement which is obtained by adding to each hyperplane $HinA$ several parallel translations of $H$ by the positive root (and its integ
A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any idea
Let $ G $ be a simple graph of $ ell $ vertices $ {1, dots, ell } $ with edge set $ E_{G} $. The graphical arrangement $ mathcal{A}_{G} $ consists of hyperplanes $ {x_{i}-x_{j}=0} $, where $ {i, j } in E_{G} $. It is well known that three properties,
By way of Ziegler restrictions we study the relation between nearly free plane arrangements and combinatorics and we give a Yoshinaga-type criterion for plus-one generated plane arrangements.