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.
From: Li Yu [view email]
[v1]
Thu, 26 Mar 2026 15:17:03 UTC (528 KB)
[v2]
Sun, 19 Jul 2026 16:21:57 UTC (468 KB)
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