A type B analog of the Ish arrangement
Copyright policy )A type B analog of the Ish arrangement
The Shi arrangement due to Shi (1986) and the Ish arrangement due to Armstrong (2013) are deformations of the type A Coxeter arrangement that share many common properties. Motivated by a question of Armstrong and Rhoades since 2012 to seek for Ish arrangements of other types, in this paper we introduce an Ish arrangement of type B . We study this Ish arrangement through various aspects similar to as known in type A with a main emphasis on freeness and supersolvability. Our method is based on the concept of ψ -digraphic arrangements recently introduced due to Abe and the authors with a type B extension.
type \(\mathrm{B}\) root system, Symmetric functions and generalizations, supersolvable arrangement, Ish arrangement, free arrangement, hyperplane arrangement, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Derivations and commutative rings, Signed and weighted graphs, Shi arrangement, vertex-weighted digraph
type \(\mathrm{B}\) root system, Symmetric functions and generalizations, supersolvable arrangement, Ish arrangement, free arrangement, hyperplane arrangement, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Derivations and commutative rings, Signed and weighted graphs, Shi arrangement, vertex-weighted digraph
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