Modular Construction of Free Hyperplane Arrangements
| Autor: | Shuhei Tsujie |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Mathematics::Combinatorics
business.industry 010102 general mathematics Dirac (software) Joins 0102 computer and information sciences Modular design 01 natural sciences Matroid Combinatorics Finite field Hyperplane 010201 computation theory & mathematics Chordal graph Simple (abstract algebra) FOS: Mathematics Mathematics - Combinatorics 52C35 05B35 05C22 13N15 Geometry and Topology Combinatorics (math.CO) 0101 mathematics business Mathematical Physics Analysis Mathematics |
| DOI: | 10.48550/arxiv.1908.01535 |
| Popis: | In this article, we study freeness of hyperplane arrangements. One of the most investigated arrangement is a graphic arrangement. Stanley proved that a graphic arrangement is free if and only if the corresponding graph is chordal and Dirac showed that a graph is chordal if and only if the graph is obtained by "gluing" complete graphs. We will generalize Dirac's construction to simple matroids with modular joins introduced by Ziegler and show that every arrangement whose associated matroid is constructed in the manner mentioned above is divisionally free. Moreover, we apply the result to arrangements associated with gain graphs and arrangements over finite fields. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|