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arXiv · 1909.10663

The saturation number of $\cb$-bounded stable monomial ideals and their powers

Reza Abdolmaleki·Jürgen Herzog·Guangjun Zhu
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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.

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Reza Abdolmaleki, Jürgen Herzog, Guangjun Zhu. 2019-09-24. The saturation number of $\cb$-bounded stable monomial ideals and their powers. https://doi.org/10.1215/21562261-2022-0013

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