The 1/3-2/3 Conjecture for $N$-Free Ordered Sets

  • Imed Zaguia
Keywords: Ordered set, Linear extension, $N$-free, Balanced pair, 1/3-2/3 Conjecture

Abstract

A balanced pair in an ordered set $P=(V,\leq)$ is a pair $(x,y)$ of elements of $V$ such that the proportion of linear extensions of $P$ that put $x$ before $y$ is in the real interval $[1/3, 2/3]$. We prove that every finite $N$-free ordered set which is not totally ordered has a balanced pair.
Published
2012-06-06
Article Number
P29