On the topology of bi-cyclopermutohedra

@article{Deshpande2022OnTT,
  title={On the topology of bi-cyclopermutohedra},
  author={Priyavrat Deshpande and Naageswaran Manikandan and Anurag Singh},
  journal={Indian Journal of Pure and Applied Mathematics},
  year={2022}
}
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 $\{1,\cdots, n+1\}$ 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… 

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