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 .
Funding statement: 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.
We also thank the two anonymous referees of this paper for their very useful corrections and suggestions.
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