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This area also includes one of order theory's most famous open problems, the [[1/3–2/3 conjecture]], which states that in any finite partially ordered set <math>P</math> that is not [[Total order|totally ordered]] there exists a pair <math>(x, y)</math> of elements of <math>P</math> for which the linear extensions of <math>P</math> in which <math>x < y</math> number between 1/3 and 2/3 of the total number of linear extensions of <math>P.</math><ref>{{citation|author=[[Sergey Kislitsyn|Kislitsyn, S. S.]] |year=1968|title=Finite partially ordered sets and their associated sets of permutations|journal=Matematicheskie Zametki|volume=4|pages=511–518}}.</ref><ref>{{citation
| last = Brightwell | first = Graham R.
| doi = 10.1016/S0012-365X(98)00311-2
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