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arXiv · 2603.25540

On Stanley-Reisner Rings with Minimal Betti Numbers

Pimeng Dai·Li Yu
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Abstract

We classify simplicial complexes with a given number of vertices whose Stanley-Reisner ring has the minimal sum of Betti numbers. The Betti numbers of the Stanley-Reisner rings of such kind of simplicial complexes are given by the binomial coefficients. We obtain a topological characterization of these simplicial complexes K by showing that any full subcomplex of K is homotopy equivalent either to a point or to a sphere. Moreover, we prove that such kind of simplicial complexes coincide with simplicial complexes having a minimal Taylor resolution. This allows us to characterize these simplicial complexes in a purely combinatorial way.

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Pimeng Dai, Li Yu. 2026-03-26. On Stanley-Reisner Rings with Minimal Betti Numbers. https://arxiv.org/abs/2603.25540

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