The saturation number of \(\mathbf{c}\)-bounded stable monomial ideals and their powers

DOI10.1215/21562261-2022-0013zbMATH Open1503.13011arXiv1909.10663OpenAlexW4285613170MaRDI QIDQ2093550

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Publication date: 27 October 2022

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Abstract: Let $S=K[x_1,ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. In this paper, we compute the socle of $cb$-bounded strongly stable ideals and determine that the saturation number of strongly stable ideals and of equigenerated $cb$-bounded strongly stable ideals. We also provide explicit formulas for the saturation number $sat(I)$ of Veronese type ideals $I$. Using this formula, we show that $sat(I^k)$ is quasi-linear from the beginning and we determine the quasi-linear function explicitly.

Full work available at URL: https://arxiv.org/abs/1909.10663

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