Arrangements of ideal type are inductively free
| Autor: | Anne Schauenburg, Gerhard Röhrle, Michael Cuntz |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
20F55
52B30 52C35 14N20 Pure mathematics Ideal (set theory) General Mathematics 010102 general mathematics Root (chord) Group Theory (math.GR) 01 natural sciences Ideal type Set (abstract data type) 0103 physical sciences FOS: Mathematics Mathematics - Combinatorics 010307 mathematical physics Combinatorics (math.CO) 0101 mathematics Mathematics - Group Theory Mathematics |
| DOI: | 10.48550/arxiv.1711.09760 |
| Popis: | Extending earlier work by Sommers and Tymoczko, in 2016 Abe, Barakat, Cuntz, Hoge, and Terao established that each arrangement of ideal type $\mathcal{A}_\mathcal{I}$ stemming from an ideal $\mathcal{I}$ in the set of positive roots of a reduced root system is free. Recently, R\"ohrle showed that a large class of the $\mathcal{A}_\mathcal{I}$ satisfy the stronger property of inductive freeness and conjectured that this property holds for all $\mathcal{A}_\mathcal{I}$. In this article, we confirm this conjecture. Comment: 10 pages. arXiv admin note: text overlap with arXiv:1606.00617 |
| Databáze: | OpenAIRE |
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