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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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
Keywords
- Moduli space of planar polygons
- Discrete Morse theory
- Homology
- Permutohedron
- Poset of ordered partitions