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arXiv · 2102.13102

Shellability and homology of $q$-complexes and $q$-matroids

Sudhir R. Ghorpade·Rakhi Pratihar·Tovohery H. Randrianarisoa
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Abstract

We consider a $q$-analogue of abstract simplicial complexes, called $q$-complexes, and discuss the notion of shellability for such complexes. It is shown that $q$-complexes formed by independent subspaces of a $q$-matroid are shellable. Further, we explicitly determine the homology of $q$-complexes corresponding to uniform $q$-matroids. We also outline some partial results concerning the determination of homology of arbitrary shellable $q$-complexes..

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Sudhir R. Ghorpade, Rakhi Pratihar, Tovohery H. Randrianarisoa. 2021-05-18. Shellability and homology of $q$-complexes and $q$-matroids. https://arxiv.org/abs/2102.13102

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