On the topology of bi-cyclopermutohedra

Priyavrat Deshpande (), Naageswaran Manikandan () and Anurag Singh ()
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Priyavrat Deshpande: Chennai Mathematical Institute
Naageswaran Manikandan: Humboldt Universität zu Berlin
Anurag Singh: Indian Institute of Technology Bhilai

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 1, 159-181

Abstract: 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 $$\{1,\dots , n+1\}$$ { 1 , ⋯ , 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 $$\mathrm {QP}_{n+1}$$ QP n + 1 . The complex $$\mathrm {QP}_{n+1}$$ QP n + 1 contains subcomplexes homeomorphic to moduli space of certain planar polygons with $$n+1$$ n + 1 sides up to isometries. In this article we find an optimal discrete Morse function on $$\mathrm {QP}_{n+1}$$ QP n + 1 and use it to compute its homology with $${\mathbb {Z}}$$ Z as well as $${\mathbb {Z}}_2$$ Z 2 coefficients.

Keywords: Moduli space of planar polygons; Discrete Morse theory; Homology; Permutohedron; Poset of ordered partitions; 51M20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00241-w

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