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arXiv · 2507.22497

Monomial polarization and depolarization of abstract simplicial complexes

Víctor M. López-Antón·Pablo Munarriz-Senosiain·Patricia Pascual-Ortigosa·Eduardo Sáenz-de-Cabezón
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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.

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Víctor M. López-Antón, Pablo Munarriz-Senosiain, Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón. 2025-07-30. Monomial polarization and depolarization of abstract simplicial complexes. https://arxiv.org/abs/2507.22497

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