Freeness for restriction arrangements of the extended Shi and Catalan arrangements

2021/11/05 by Norihiro Nakashima, Nakashima, Norihiro, Shuhei Tsujie +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation #Primary 32S22 #Secondary 52C35

paper · pdf · doi:10.48550/arxiv.2111.03585

openalex publication_date 2021/11/05 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

The extended Shi and Catalan arrangements are well investigated arrangements. In this paper, we prove that the cone of the extended Catalan arrangement of type A is always hereditarily free, while we determine the dimension in which the cone of the extended Shi arrangement of type A is hereditarily free. For this purpose, using digraphs, we define a class of arrangements which is closed under restriction, and which contains the extended Shi and Catalan arrangements. We also characterize the freeness for the cone of this arrangement by graphical conditions.

Related

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