An Empirically Fast Las Vegas Algorithm for Algebraic Shifting

TL;DR

This paper introduces a faster Las Vegas algorithm for algebraic shifting of hypergraphs and simplicial complexes, especially effective in positive characteristic, with practical improvements demonstrated through experiments.

Contribution

It presents a novel, empirically faster algorithm for algebraic shifting, extending practical computability for a wider class of complexes.

Findings

Algorithm significantly improves computation speed in positive characteristic.

Implementation in OSCAR successfully handles various complex inputs.

Extends the range of complexes for which algebraic shifting is feasible.

Abstract

Improved algorithms for computing (partial and full) exterior algebraic shifts of hypergraphs and simplicial complexes are presented. The main benefit is in positive characteristic. Experiments with an implementation in OSCAR with various inputs such as bipartite graphs and triangulations of two and three dimensional manifolds show that the method considerably extends for which simplicial complexes exterior algebraic shifts can be computed in practice.