Regularity of symbolic powers and arboricity of matroids

Nguyên Công Minh 1  and Trân Nam Trung 2
  • 1 Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam
  • 2 Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
Nguyên Công Minh
  • Corresponding author
  • Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam
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and Trân Nam Trung

Abstract

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*.

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