2 papers
math.AC2026
On Stanley-Reisner Rings with Minimal Betti Numbers
Pimeng Dai, Li Yu
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…
math.CO2024
On Simplicial Complexes with Extremal Total Betti number and Total Bigraded Betti Number
Pimeng Dai, Li Yu
We determine which simplicial complexes have the maximum or minimum sum of Betti numbers and sum of bigraded Betti numbers with a given number of vertices in each dimension.