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Balancing extensions via Brunn-Minkowski
Authors:Jeff Kahn  Nathan Linial
Affiliation:1. Department of Mathematics and Center for Operations Research, Rutgers University, 08903, New Brunswick, NJ, USA
2. Institute of Mathematics and Computer Sci, The Hebrew University, 91904, Jerusalem, Israel
3. IBM Research Almaden, 650 Harry Rd., 95120, San Jose, Ca, USA
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

$$1/2e< p(x< y)< 1 - 1/2e.$$
Keywords:  KeywordHeading"  >AMS subject classification (1991) 06 A 07  52 A 38  68 P 10  68 R 05
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