Balancing extensions via Brunn-Minkowski

Combinatorica volume 11, pages363–368(1991)Cite this article

Abstract

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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Author information

Affiliations

  1. Department of Mathematics and Center for Operations Research, Rutgers University, 08903, New Brunswick, NJ, USA

    Jeff Kahn

  2. Institute of Mathematics and Computer Sci, The Hebrew University, 91904, Jerusalem, Israel

    Nathan Linial

  3. IBM Research Almaden, 650 Harry Rd., 95120, San Jose, Ca, USA

    Nathan Linial

Authors
  1. Jeff Kahn
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  2. Nathan Linial
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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). https://doi.org/10.1007/BF01275670

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AMS subject classification (1991)

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