Brightwell, Graham (1999) Balanced pairs in partial orders. Discrete mathematics, 201 (1-3). pp. 25-52. ISSN 0012-365X
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/rights/LSERO.htm |
| URL: | http://eprints.lse.ac.uk/7481/ |
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