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Balanced pairs in partial orders

Brightwell, Graham (1999) Balanced pairs in partial orders. Discrete Mathematics, 201 (1-3). pp. 25-52. ISSN 0012-365X

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Abstract

An α-balanced pair in a partially ordered set P = (X, <) is a pair (x, y) of elements of X such that the proportion of linear extensions of P with x below y lies between α and 1 − α. The 1/3–2/3 Conjecture states that, in every finite partial order P, not a chain, there is a 1/3-balanced pair. This was first conjectured in a 1968 paper of Kislitsyn, and remains unsolved. We survey progress towards a resolution of the conjecture, and discuss some of the many related problems.

Item Type: Article
Official URL: http://www.elsevier.com/locate/disc
Additional Information: © 1999 Elsevier Science B.V.
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 17 Feb 2010 14:27
URL: http://eprints.lse.ac.uk/7481/

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