An Application of Dumont's Statistic

Mark Skandera

MIT

April 26,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

In 1974, Dumont gave an interpretation of the Eulerian numbers which extends to a number of statistics on permutations and on arbitrary words. We apply one such statistic to a special case of a result of Stanley concerning the flag h-vectors of balanced Cohen-Macaulay complexes. 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.


Speaker's Contact Info: skan(at-sign)math.mit.edu


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