Arithmetical Ranks of Stanley–Reisner Ideals of Simplicial Complexes with a Cone

Arithmetical ranks of Stanley-Reisner ideals of simplicial complexes with a cone

When a cone is added to a simplicial complex ∆ over one of its faces, we investigate the relation between the arithmetical ranks of the StanleyReisner ideals of the original simplicial complex and the new simplicial complex ∆′. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of ∆′ equals the projective dimension of the Stanley-Reisner ring of ∆′ if the correspondi...

an investigation of the types of text reduction in subtitling: a case study of the persian film gilaneh with english subtitles

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On Isomorphism of Simplicial Complexes and Their Related Algebras

Minors of simplicial complexes

We extend the notion of a minor from matroids to simplicial complexes. We show that the class of matroids, as well as the class of independence complexes, is characterized by a single forbidden minor. Inspired by a recent result of Aharoni and Berger, we investigate possible ways to extend the matroid intersection theorem to simplicial complexes.

Representing Simplicial Complexes with Mangroves

Simplicial complexes are extensively used for discretizing digital shapes in two, three, and higher dimensions within a variety of application domains. There have been many proposals of topological data structures, which represent the connectivity information among simplices. We introduce the Mangrove Topological Data Structure (Mangrove TDS) framework, a tool which supports the efficient imple...