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Balancing extensions via Brunn-Minkowski

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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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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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  • DOI: https://doi.org/10.1007/BF01275670

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