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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Multiple addition, deletion and restriction theorems for hyperplane arrangements
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by Takuro Abe and Hiroaki Terao PDF
Proc. Amer. Math. Soc. 147 (2019), 4835-4845 Request permission

Abstract:

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.
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Additional Information
  • Takuro Abe
  • Affiliation: Institute of Mathematics for Industry, Kyushu University, Fukuoka 819-0395, Japan
  • Email: abe@imi.kyushu-u.ac.jp
  • Hiroaki Terao
  • Affiliation: Department of Mathematics, Hokkaido University, Hokkaido 060-0808, Japan
  • MR Author ID: 191642
  • Email: terao@math.sci.hokudai.ac.jp
  • Received by editor(s): January 22, 2018
  • Received by editor(s) in revised form: February 10, 2019
  • Published electronically: June 10, 2019
  • Additional Notes: The first author was partially supported by KAKENHI, JSPS Grant-in-Aid for Scientific Research (B) 16H03924, and Grant-in-Aid for Exploratory Research 16K13744.
  • Communicated by: Patricia Hersh
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4835-4845
  • MSC (2010): Primary 32S22; Secondary 52C35
  • DOI: https://doi.org/10.1090/proc/14592
  • MathSciNet review: 4011517