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An Application of Dumont’s Statistic

In: Formal Power Series and Algebraic Combinatorics

Author

Listed:
  • M. Skandera

    (Institute of Technology Cambridge, Department of Mathematics Massachusetts)

Abstract

In 1974, Dumont [5] gave an interpretation of the Eulerian numbers which extends to a number of statistics on permutations [7] and on arbitrary words [8]. We apply one such statistic to a special case of a result of Stanley concerning the flag h-vectors of Cohen-Macaulay complexes [9]. Specifically, we give a bijective proof that for each distributive lattice J(P) which is a product of chains, there is a poset Q such that the f-vector of Q is the h-vector of P. We conjecture that the result holds for all finite distributive lattices.

Suggested Citation

  • M. Skandera, 2000. "An Application of Dumont’s Statistic," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 743-753, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_73
    DOI: 10.1007/978-3-662-04166-6_73
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