Regularity of symbolic powers and Arboricity of matroids

2017/02/15 by Minh, Nguyen Cong, Trung, Tran Nam
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.04491

Abstract

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

Related

• The Structure of Symbolic Powers of Matroids
• The cleanness of (symbolic) powers of Stanley-Reisner ideals
• Regularity of symbolic powers of square-free monomial ideals
• Slightly mixed symbolic powers of matroids are locally glicci
• Upper bounds for the regularity of symbolic powers of certain classes of edge ideals