elements of some (finite) poset , write for the probability that precedes in a random (uniform) linear extension of . For define
where the infimum is over all choices of and distinct .
Addressing an issue raised by Fishburn [6], we give the first nontrivial lower bounds on the function . This is part of a more general geometric result, the exact determination of the function
where the infimum is over chosen uniformly from some compact convex subset of a Euclidean space.
These results are mainly based on the Brunn–Minkowski Theorem and a theorem of Keith Ball [1], which allow us to reduce to a 2-dimensional version of the problem.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: October 6, 1997
Rights and permissions
About this article
Cite this article
Kahn, J., Yu, Y. Log-Concave Functions And Poset Probabilities. Combinatorica 18, 85–99 (1998). https://doi.org/10.1007/PL00009812
Issue Date:
DOI: https://doi.org/10.1007/PL00009812