English

Homotopy type of shellable $q$-complexes and their homology groups

Combinatorics 2024-03-13 v1

Abstract

The theory of shellable simplicial complexes brings together combinatorics, algebra, and topology in a remarkable way. Initially introduced by Alder for qq-simplicial complexes, recent work of Ghorpade, Pratihar, and Randrianarisoa extends the study of shellability to qq-matroid complexes and determines singular homology groups for a subclass of these qq-simplicial complexes. In this paper, we determine the homotopy type of shellable qq-simplicial complexes. Moreover, we establish the shellability of order complexes from lexicographically shellable qq-simplicial complexes, that include the qq-matroid complexes. This results in a comprehensive determination of the homology groups for any lexicographically shellable qq-complexes.

Keywords

Cite

@article{arxiv.2403.07102,
  title  = {Homotopy type of shellable $q$-complexes and their homology groups},
  author = {Sudhir R. Ghorpade and Rakhi Pratihar and Tovohery H. Randrianarisoa and Hugues Verdure and Glen Wilson},
  journal= {arXiv preprint arXiv:2403.07102},
  year   = {2024}
}

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25 pages