Balancing extensions via Brunn-Minkowski


We give a simple proof, based on the Brunn-Minkowski Theorem, of Theorem. Inany finite poset P not a total order there are elementsx, y such that

$$1/2e< p(x< y)< 1 - 1/2e.$$

A similar result was independently found by A. Karzanov and L. G. Khachiyan

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Additional information

Supported by NSF Grant MCS 83-01867, AFOSR Grant 0271, and a Sloan Research Fellowship. This research was done while the author was visiting IBM Research Almaden.

Supported in part by grants from the Israel-US Binational Science Foundation and the Israeli Academy of Sciences.

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Kahn, J., Linial, N. Balancing extensions via Brunn-Minkowski. Combinatorica 11, 363–368 (1991).

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AMS subject classification (1991)

  • 06 A 07
  • 52 A 38
  • 68 P 10
  • 68 R 05