On a special class of Stanley-Reisner ideals

Document Type: Research Paper


Kharazmi University


For an $n$-gon with vertices at points $1,2,\cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, we
generalize this result to find the minimal free resolution and Betti numbers of the $S$-module $S/I$ where  $S=K[x_{1},\cdots, x_{n}]$ and $I$ is the associated ideal to the generalized suspension of it in the Stanley-Reisner sense. Applications to Stanley-Reisner ideals and simplicial complexes are considered.