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Polyspherical Complexes
Gábor Hetyei
Department of Mathematics and Statistics, University of North Carolina, Charlotte NC 28223, USA.
ghetyei@uncc.edu
Annals of Combinatorics 9 (4) p.379-409 December, 2005
AMS Subject Classification: 05E35, 06A07, 57Q05
Abstract:
We construct spherical CW-complexes whose face structure may be conveniently described using a system of polyspherical coordinates introduced by Vilenkin, Kuznetsov and Smorodinskii. We show that these complexes may be constructed by repeated use of CW-suspension, free join, and edge subdivision. We prove that all CW-spheres constructed in this way have non-negative cd-index and thus verify Stanley's famous conjecture. Among the particular examples we find a new class of partially ordered sets whose order complexes encode the derivative polynomials for secant of even degree. The geometric constructions presented in this paper generalize CW-complexes introduced whose flag numbers are suitable to encode systems of orthogonal polynomials.
Keywords: partially ordered set, Eulerian, flag, polyspherical coordinates, derivative polynomial

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