论文信息 - Log-Concave Functions And Poset Probabilities

Log-Concave Functions And Poset Probabilities

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.

Jeff Kahn | Yang Yu

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