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Abstract
We prove a conjecture of Stanley on thecd-index of the semisuspension of the face poset of a simplicial shelling component. We give a new signed generalization of André permutations, together with a new notion ofcd-variation for signed permutations. This generalization not only allows us to compute thecd-index of the face poset of a cube, but also occurs as a natural set of orbit representatives for a signed generalization of the Foata-Strehl commutative group action on the symmetric group. From the induction techniques used, it becomes clear that there is more than one way to define classes of permutations andcd-variation such that they allow us to compute thecd-index of the same poset.
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G. Hetyei
Present address: Mathematical Research Institute of the Hungarian Academy of Sciences, Hungary
Authors and Affiliations
LACIM, Département de mathématiques, Université du Québec à Montréal, Case postale 8888, succursale Centre-Ville, H3C 3P8, Montréal, Québec, Canada
G. Hetyei
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This research was supported by the UQAM Foundation.
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Hetyei, G. On thecd-variation polynomials of André and simsun permutations.Discrete Comput Geom16, 259–275 (1996). https://doi.org/10.1007/BF02711512
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