The toric h-vectors of partially ordered sets

Margaret M. Bayer, Richard Ehrenborg

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


An explicit formula for the toric /i-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, gn/2(P) = gn/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.

Original languageEnglish
Pages (from-to)4515-4531
Number of pages17
JournalTransactions of the American Mathematical Society
Issue number10
StatePublished - 2000


  • Cd-index. Coaleebra
  • Partially ordered set. H-vector

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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