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

Identification Number: 10.1016/S0012-365X(98)00311-2

## 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 |
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Official URL: | http://www.elsevier.com/locate/disc |

Additional Information: | © 1999 Elsevier Science B.V. |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 17 Feb 2010 14:27 |

Last Modified: | 01 Oct 2010 08:59 |

URI: | http://eprints.lse.ac.uk/id/eprint/7481 |

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