Centre for Discrete and Applicable Mathematics
	CDAM Research Report, LSE-CDAM-98-14 June 1998

Abstract

An  alpha-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  alpha  and   1 - alpha.  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.

A compressed (gzip) PostScript file (121 kB) with the full contents of this report can be downloaded by clicking here.

Alternatively, if you like a free hard copy of this report, please send the number of this report, LSE-CDAM-98-14, together with your name and postal address to:

		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-171-955 7732. Fax: +44(0)-171-955 6877. Email: info@maths.lse.ac.uk

		Introduction to the CDAM Research Report Series.
		CDAM Homepage.

Last changed: Wed 9 Feb 2005
For comments go to: http://www.maths.lse.ac.uk/webmaster.html