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A type $B$ analog of the Ish arrangement
Tran, Tan N.1; Tsujie, Shuhei2
1 Binghamton University (SUNY) Department of Mathematics and Statistics Binghamton NY 13902-6000 USA
2 Hokkaido University of Education Department of Mathematics Asahikawa Hokkaido 070-8621 Japan
Algebraic Combinatorics, Volume 8 (2025) no. 1, pp. 267-294.

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 $\psi $-digraphic arrangements recently introduced due to Abe and the authors with a type $B$ extension.

Received:
Accepted:
Published online:
DOI: 10.5802/alco.405
Classification: 52C35, 05C22, 13N15
Keywords: Hyperplane arrangement, free arrangement, supersolvable arrangement, Shi arrangement, Ish arrangement, type B root system, vertex-weighted digraph

Tran, Tan N. 1; Tsujie, Shuhei 2

1 Binghamton University (SUNY) Department of Mathematics and Statistics Binghamton NY 13902-6000 USA
2 Hokkaido University of Education Department of Mathematics Asahikawa Hokkaido 070-8621 Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Tran, Tan N.; Tsujie, Shuhei. A type $B$ analog of the Ish arrangement. Algebraic Combinatorics, Volume 8 (2025) no. 1, pp. 267-294. doi : 10.5802/alco.405. https://alco.centre-mersenne.org/articles/10.5802/alco.405/

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