Geodesic
The \(1/3\)-\(2/3\) conjecture for \(N\)-free ordered sets
Imed Zaguia1
1Dept of Mathematics & Computer Science, Royal Military College of Canada
The electronic journal of combinatorics, Tome 19 (2012) no. 2
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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.
DOI : 10.37236/2345
Classification : 06A06, 06A05
Mots-clés : ordered set, linear extension, \(N\)-free, balanced pair, \(1/3\)-\(2/3\) conjecture

Imed Zaguia  1

1 Dept of Mathematics & Computer Science, Royal Military College of Canada 
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     author = {Imed Zaguia},
     title = {The \(1/3\)-\(2/3\) conjecture for {\(N\)-free} ordered sets},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {2},
     doi = {10.37236/2345},
     zbl = {1288.06005},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2345/}
}
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Imed Zaguia. The \(1/3\)-\(2/3\) conjecture for \(N\)-free ordered sets. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2345

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