Bases for the Flag f-Vectors of Eulerian Posets

Nathan Reading

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


Abstract

We investigate various bases for the flag f-vectors of Eulerian posets. Many of the change-of-basis formulas are seen to be triangular. One change-of-basis formula implies the following: If the Charney-Davis Conjecture is true for order complexes, then certain sums of cd-coefficients are non-negative in all Gorenstein* posets. In particular, cd-coefficients with no adjacent c's are non-negative. A convolution formula for cd-coefficients, together with the proof by M.~Davis and B.~Okun of the Charney-Davis Conjecture in dimension 3, imply that certain additional cd-coefficients are non-negative for all Gorenstein* posets. In particular we verify, up to rank 6, Stanley's conjecture that the coefficients in the cd-index of a Gorenstein* ranked poset are non-negative.


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