An Empirically Fast Las Vegas Algorithm for Algebraic Shifting

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.