2019/04/27 by Priyavrat Deshpande, Deshpande, Priyavrat, Naageswaran Manikandan +3
Materials Science · Mathematics · #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.1904.12183
openalex publication_date 2019/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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,⋯, 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 QPn+1. The complex QPn+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 QPn+1 and use it to compute its homology with ℤ as well as ℤ2 coefficients.