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arXiv · 2111.10851

Shedding vertices and Ass-decomposable monomial ideals

Raheleh Jafari·Ali Akbar Yazdan Pour
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Abstract

The shedding vertices of simplicial complexes are studied from an algebraic point of view. Based on this perspective, we introduce the class of ass-decomposable monomial ideals which is a generalization of the class of Stanley-Reisner ideals of vertex decomposable simplicial complexes. The recursive structure of ass-decomposable monomial ideals allows us to find a simple formula for the depth, and in squarefree case, an upper bound for the regularity of such ideals.

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Raheleh Jafari, Ali Akbar Yazdan Pour. 2023-05-30. Shedding vertices and Ass-decomposable monomial ideals. https://doi.org/10.1216/rmj.2023.53.89

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