On log concavity for order-preserving maps of partial orders

David E. Daykin, Jacqueline W. Daykin, Michael S. Paterson

Research output: Contribution to journalArticlepeer-review


Stanley used the Aleksandrov-Fenchel inequalities from the theory of mixed volumes to prove the following results. Let P be a partially ordered set with n elements, and let x ε{lunate} P, If N i * is the number of linear extension λ : P → {1, 2, ..., n} satisfying λ(x) = i, then the sequence N 1 *, ..., N n * is log concave (and therefore unimodal). Here the analogous results for both strict order-preserving and order-preserving maps are proved using an explicit injection. Further, if ν c is the number of strict order-preserving maps of P into a chain of length c, then ν c is shown to be log concave, and the corresponding result is established for order-preserving maps.

Original languageEnglish
Pages (from-to)221-226
Number of pages6
JournalDiscrete Mathematics
Issue numberC
Publication statusPublished - 1984
Externally publishedYes


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