A new symmetric resolution for $(x_{1},\dots, x_{n})^{n}$

Abstract

Let $S=k[x_1,\cdots,x_n]$ be a polynomial ring over an arbitrary field $k$. We construct a new symmetric polytopal minimal resolution of $(x_1,\cdots,x_n)^n$. Using this resolution, we also obtain a symmetric polytopal minimal resolution of the ideal obtained by removing $x_1\cdots x_n$ from the generators of $(x_1,\cdots,x_n)^n$.