Department of Mathematics

Combinatorics and Graph Theory

  •  Swee Hong Chan, University of California, Los Angeles
  •  Log-concavity, cross product conjectures, and FKG inequalities in order theory
  •  03/22/2023
  •  3:00 PM - 3:50 PM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Bruce E Sagan (

Given a finite poset that is not completely ordered, is it always possible to find two elements x and y, such that the probability that x is less than y in the random linear extension of the poset, is bounded away from 0 and 1? Kahn-Saks gave an affirmative answer and showed that this probability falls between 3/11 (0.273) and 8/11 (0.727). The currently best known bound is 0.276 and 0.724 by Brightwell-Felsner-Trotter, and it is believed that the optimal bound should be 1/3 and 2/3, also known as the 1/3-2/3 Conjecture. Most notably, log-concave and cross product inequalities played the central role in deriving both bounds. In this talk we will discuss various generalizations of these results together with related open problems. This talk is joint work with Igor Pak and Greta Panova, and is intended for the general audience.



Department of Mathematics
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