On a special class of Stanley-Reisner ideals

For an n-gon with vertices at points ۱,۲,\cdots,n, the Betti numbers of its suspension, the simplicial complex that involves two more vertices n+۱ and n+۲, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the S-module S/I where  S=K[x_{۱},\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.

Keywords:

Betti numbers , Stanley , graded Betti numbers , Reisner ideal , graded minimal free resolution , Stanley-Reisner ideal , simplicial complexes