Combinatorica

, Volume 18, Issue 1, pp 85–99

Log-Concave Functions And Poset Probabilities

  • Jeff Kahn
  • Yang Yu
Original Paper

DOI: 10.1007/PL00009812

Cite this article as:
Kahn, J. & Yu, Y. Combinatorica (1998) 18: 85. doi:10.1007/PL00009812

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.

AMS Subject Classification (1991) Classes:  52A40, 52C07, 06A07 

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Copyright information

© János Bolyai Mathematical Society, 1998

Authors and Affiliations

  • Jeff Kahn
    • 1
  • Yang Yu
    • 2
  1. 1.Department of Mathematics and RUTCOR, Rutgers University; Piscataway, NJ 08854; E-mail: jkahn@math.rutgers.eduUS
  2. 2.Department of Mathematics, Rutgers University; Piscataway, NJ 08854; E-mail: yangyu@math.rutgers.eduUS

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