The toric h-vectors of partially ordered sets [9 citations — 5 self]
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by Margaret M. Bayer, Richard Ehrenborg
Trans. Amer. Math. Soc
http://titania.math.ukans.edu/~reports/1998/papers/980301.bayer.ps.gz
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Abstract:
Abstract. An explicit formula for the toric h-vector of an Eulerian poset in terms of the cd-index is developed using coalgebra techniques. The same techniques produce a formula in terms of the flag h-vector. For this another proof based on Fine's algorithm and lattice-path counts is given. As a consequence, it is shown that the Kalai relation on dual posets, g n=2 (P) = g n=2 (P), is the only equation relating the h-vectors of posets and their duals. A result on the h-vectors of oriented matroids is given. A simple formula for the cd-index in terms of the flag h-vector is derived. 1.
