Computation of Poincaré-Betti Series for Monomial Rings

Abstract

The multigraded Poincaré-Betti series $P^kR(\bar{x}; t) of a monomial ring $k[\bar{x}]/\langle M\rangle$ on a finite number of monomial generators has the form $\prod_{x_i\in\bar{x}}(1+x_i t)/b_{R,k}(\bar{x};t)$, where $b_{R,k}(\bar{x};t)$ is a polynomial depending only on the monomial set M and the characteristic of the field k. I present a computer program designed to calculate the polynomial $b_{R,k} for a given field characteristic and a given set of monomial generators.