A strong log-concavity property for measures on Boolean algebras

J. Kahn, M. Neiman

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1749-1760
Number of pages12
JournalJournal of Combinatorial Theory. Series A
Volume118
Issue number6
DOIs
StatePublished - Aug 2011

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Keywords

  • Antipodal pairs property
  • Johnson scheme
  • Log-concavity
  • Mason's conjecture
  • Negative correlation

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