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

By Imed Zaguia


A balanced pair in an ordered set P = (V,�) 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

Topics: Ordered set, Linear extension, N-free, Balanced pair, 1/3-2/3 Conjecture
Year: 2013
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