Abstract

In this paper, we will describe the Pascal Type properties of Betti numbers of ideals associated to n-gons. These are quite similar to the properties enjoyed by the Pascal's Triangle, concerning the binomial coefficients. By definition, the Betti numbers βt(n) of an ideal I associated to an n-gon are the ranks of the modules in a free minimal resolution of the R-module R/I, where R is the polynomial ring k[x1,x2,…,xn]. Here k is any field and x1,x2,…,xn are indeterminates. We will prove those properties using a specific formula for the Betti numbers.