A strong log-concavity property for measures on Boolean algebras

Details A strong log-concavity property for measures on Boolean algebras A strong log-concavity property for measures on Boolean algebras

2009-07-01

arxiv.org/abs/0907.0243v1

Mathematics

Combinatorics

13 pages

Scientific paper

We introduce the antipodal pairs property for probability measures on finite Boolean algebras and prove that conditional versions imply strong forms of log-concavity. We give several applications of this fact, including improvements of some results of Wagner; a new proof of a theorem of Liggett stating that ultra-log-concavity of sequences is preserved by convolutions; and some progress on a well-known log-concavity conjecture of J. Mason.

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