Monomial polarization and depolarization of abstract simplicial complexes
Commutative Algebra
2025-07-31 v1 Algebraic Topology
Abstract
We translate the operations of polarization and depolarization from monomial ideals in a polynomial ring to abstract simplicial complexes. As a result, we explicitly describe the relation between the Koszul simplicial complex of a monomial ideal and that of its polarization. Using the simplicial translation of depolarization we propose a way to reduce a simplicial complex to a smaller one with the same homology. This type of reduction, that can be interpreted as non-elementary collapse, can be used as a pre-process step for algorithms on simplicial complexes. We apply this methodology to the efficient computation of the Alexander dual of abstract simplicial complexes.
Keywords
Cite
@article{arxiv.2507.22497,
title = {Monomial polarization and depolarization of abstract simplicial complexes},
author = {Víctor M. López-Antón and Pablo Munarriz-Senosiain and Patricia Pascual-Ortigosa and Eduardo Sáenz-de-Cabezón},
journal= {arXiv preprint arXiv:2507.22497},
year = {2025}
}