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Forum Mathematicum

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Volume 31, Issue 2


Regularity of symbolic powers and arboricity of matroids

Nguyên Công Minh
  • Corresponding author
  • Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam
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/ Trân Nam Trung
Published Online: 2018-10-30 | DOI: https://doi.org/10.1515/forum-2017-0243


Let Δ be a matroid complex. In this paper, we explicitly compute the regularity of all the symbolic powers of its Stanley–Reisner ideal in terms of combinatorial data of Δ. In order to do that, we provide a sharp bound between the arboricity of Δ and the circumference of its dual Δ*.

Keywords: Matroid; arboricity; circumference; Stanley–Reisner ideal; Castelnuovo–Mumford regularity

MSC 2010: 13D45; 05E40; 05E45


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About the article

Received: 2017-11-21

Revised: 2018-09-28

Published Online: 2018-10-30

Published in Print: 2019-03-01

This paper was done while the first author was visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the VIASM for the hospitality and financial support, and he also thanks the Vietnam National Foundation for Science and Technology Development (NAFOSTED) for its support under grant number 101.01-2016.21.

Citation Information: Forum Mathematicum, Volume 31, Issue 2, Pages 465–477, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0243.

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