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On the topology of bi-cyclopermutohedra

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Abstract

Motivated by the work of Panina and her coauthors on cyclopermutohedron we study a poset whose elements correspond to equivalence classes of partitions of the set \(\{1,\dots , n+1\}\) up to cyclic permutations and orientation reversion. This poset is the face poset of a regular CW complex which we call bi-cyclopermutohedron and denote it by \(\mathrm {QP}_{n+1}\). The complex \(\mathrm {QP}_{n+1}\) contains subcomplexes homeomorphic to moduli space of certain planar polygons with \(n+1\) sides up to isometries. In this article we find an optimal discrete Morse function on \(\mathrm {QP}_{n+1}\) and use it to compute its homology with \({\mathbb {Z}}\) as well as \({\mathbb {Z}}_2\) coefficients.

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Authors and Affiliations

  1. Chennai Mathematical Institute, Chennai, India

    Priyavrat Deshpande

  2. Humboldt Universität zu Berlin, Berlin, Germany

    Naageswaran Manikandan

  3. Indian Institute of Technology Bhilai, Sejbahar, India

    Anurag Singh

Authors
  1. Priyavrat Deshpande
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  2. Naageswaran Manikandan
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  3. Anurag Singh
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Corresponding author

Correspondence to Anurag Singh.

Additional information

Communicated by Rahul Roy.

The first author is partially funded by a grant from the Infosys Foundation and by the MATRICS Grant MTR/2017/000239.

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Deshpande, P., Manikandan, N. & Singh, A. On the topology of bi-cyclopermutohedra. Indian J Pure Appl Math 54, 159–181 (2023). https://doi.org/10.1007/s13226-022-00241-w

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  • DOI: https://doi.org/10.1007/s13226-022-00241-w

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