An alternative algorithm for computing the Betti table of a monomial ideal

TL;DR

This paper introduces a new algorithm for computing the Betti table of monomial ideals, demonstrating promising efficiency through implementation and experiments, and establishing new constraints on Betti table shapes.

Contribution

The paper presents a novel algorithm for Betti table computation and proves new constraints on their possible shapes, improving understanding and efficiency.

Findings

Prototype implementation shows promising efficiency

Numerical experiments validate the algorithm's performance

New constraints on Betti table shapes are established

Abstract

In this paper we develop a new technique to compute the Betti table of a monomial ideal. We present a prototype implementation of the resulting algorithm and we perform numerical experiments suggesting a very promising efficiency. On the way of describing the method, we also prove new constraints on the shape of the possible Betti tables of a monomial ideal.