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About: 1/3–2/3 conjecture     Goto   Sponge   NotDistinct   Permalink

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Type: companyyago:WikicatConjecturesyago:Abstraction100002137yago:Cognition100023271yago:Concept105835747yago:Content105809192yago:Hypothesis105888929yago:Idea105833840yago:PsychologicalFeature100023100yago:Speculation105891783 New Facet based on Instances of this Class

In order theory, a branch of mathematics, the 1/3–2/3 conjecture states that, if one is comparison sorting a set of items then, no matter what comparisons may have already been performed, it is always possible to choose the next comparison in such a way that it will reduce the number of possible sorted orders by a factor of 2/3 or better. Equivalently, in every finite partially ordered set that is not totally ordered, there exists a pair of elements x and y with the property that at least 1/3 and at most 2/3 of the linear extensions of the partial order place x earlier than y.