2026/03/26 by Pimeng Dai, Li Yu
#math.AC #math.AT #math.CO
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.