On the extendability of free multiarrangements

2007/10/26 by Masahiko Yoshinaga, Yoshinaga, Masahiko · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #32S22 #52C35 #Advanced Algebra and Logic #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Genome Rearrangement Algorithms #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0710.5044

openalex publication_date 2007/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A free multiarrangement of rank k is defined to be extendable if it is obtained from a simple rank (k+1) free arrangement by the natural restriction to a hyperplane (in the sense of Ziegler). Not all free multiarrangements are extendable. We will discuss extendability of free multiarrangements for a special class. We also give two applications. The first is to produce totally non-free arrangements. The second is to give interpolating free arrangements between extended Shi and Catalan arrangements.

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• Extendability of the B₂-arrangement

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• Extendability of the B₂-arrangement
• Freeness for multiarrangements of hyperplanes over arbitrary fields
• Some characterizations of freeness of hyperplane arrangement
• Free arrangements and coefficients of characteristic polynomials
• Freeness for restriction arrangements of the extended Shi and Catalan arrangements