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Balanced pairs in partial orders

By Graham Brightwell

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

Topics: QA Mathematics
Publisher: Elsevier
Year: 1999
DOI identifier: 10.1016/S0012-365X(98)00311-2
OAI identifier: oai:eprints.lse.ac.uk:7481
Provided by: LSE Research Online
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