Brightwell, Graham (1999) Balanced pairs in partial orders. Discrete mathematics, 201 (1-3). pp. 25-52. ISSN 0012-365X
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.
|Additional Information:||© 1999 Elsevier Science B.V.|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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