Integral closure and Hilbert series of a special monomial ideal

Abstract

Let $R=K[x_1,\dots ,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $M_{n,t}=(x^{e_1},\dots ,x^{e_n})$ be a monomial ideal of $R$, where $x^{e_i}=x_1^t\dots x_{i-1}^t{x}_{i+1}^t\dots x_n^t$. We study the unmixedness of its integral closure. Furthermore, we compute the Hilbert series of this ideal and we show that this ideal is Freiman.

7 Pages. Comments welcome