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 |

Date Deposited: | 17 Feb 2010 14:27 |

URL: | http://eprints.lse.ac.uk/7481/ |

### Actions (login required)

Record administration - authorised staff only |