The 1/3-2/3 conjecture for $N$-free ordered sets

Details The 1/3-2/3 conjecture for $N$-free ordered sets The 1/3-2/3 conjecture for $N$-free ordered sets

2011-07-28

arxiv.org/abs/1107.5626v1

Mathematics

Combinatorics

Scientific paper

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.

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