Multiple addition, deletion and restriction theorems for hyperplane arrangements

Takuro Abe, Hiroaki Terao

研究成果: Contribution to journalArticle査読

3 被引用数 (Scopus)

抄録

In the study of free arrangements, the most useful result to construct/ check free arrangements is the addition-deletion theorem in [J. Fac. Sci. Univ. Tokyo 27 (1980), 293-320]. Recently, the multiple version of the addition theorem was proved in [J. Eur. Math. Soc. 18 (2016), 1339-1348], called the multiple addition theorem (MAT), to prove the ideal-free theorem. The aim of this article is to give the deletion version of MAT, the multiple deletion theorem (MDT). Also, we can generalize MAT to get MAT2 from the viewpoint of our new proof. Moreover, we introduce the restriction version, a multiple restriction theorem (MRT). Applications of MAT2, including the combinatorial freeness of the extended Catalan arrangements, are given.

本文言語英語
ページ(範囲)4835-4845
ページ数11
ジャーナルProceedings of the American Mathematical Society
147
11
DOI
出版ステータス出版済み - 2019

All Science Journal Classification (ASJC) codes

  • 数学 (全般)
  • 応用数学

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