%0 Journal Article
%T The 1/3-2/3 conjecture for $N$-free ordered sets
%A Imed Zaguia
%J Mathematics
%D 2011
%I arXiv
%X A balanced pair in a finite 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.
%U http://arxiv.org/abs/1107.5626v2