Poincare Series of Monomial Rings with Minimal Taylor Resolution

TL;DR

This paper compares the Poincare series of certain monomial rings and provides explicit computations for those with minimal Taylor resolutions, enhancing understanding of their algebraic properties.

Contribution

It introduces a comparison method for Poincare series of monomial rings and computes these series explicitly for rings with minimal Taylor resolutions.

Findings

Derived formulas for Poincare series of specific monomial rings.

Established relationships between Poincare series of related monomial rings.

Provided explicit computations for rings with minimal Taylor resolution.

Abstract

We give a comparison between the Poincare series of two monomial rings: $R=A/I$ and $R_q=A/I_q$ where $I_q$ is a monomial ideal generated by the $q$'th power of monomial generators of $I$. We compute the Poincare series for a class of monomial rings with minimal Taylor resolution. The paper was produced during Pragmatic 2011.