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Regularity of powers of Stanley–Reisner ideals of one‐dimensional simplicial complexes

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  • Nguyen Cong Minh
  • Thanh Vu

Abstract

Let Δ be a one‐dimensional simplicial complex. Let IΔ$I_\Delta$ be the Stanley–Reisner ideal of Δ. We prove that for all s≥1$s \ge 1$ and all intermediate ideals J generated by IΔs$I_\Delta ^s$ and some minimal generators of IΔ(s)$I_\Delta ^{(s)}$, we have regJ=regIΔs=regIΔ(s).$$\begin{equation*} \hspace*{120pt}\operatorname{reg}J = \operatorname{reg}I_\Delta ^s = \operatorname{reg}I_\Delta ^{(s)}.\hspace*{-120pt} \end{equation*}$$

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  • Nguyen Cong Minh & Thanh Vu, 2023. "Regularity of powers of Stanley–Reisner ideals of one‐dimensional simplicial complexes," Mathematische Nachrichten, Wiley Blackwell, vol. 296(8), pages 3539-3558, August.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:8:p:3539-3558
    DOI: 10.1002/mana.202100485
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