Abstract
For a finite poset P and x, yεP let pr(x>y) be the fraction of linear extensions which put x above y. N. Linial has shown that for posets of width 2 there is always a pair x, y with 1/3 ⩽ pr(x>y)⩽2/3. The disjoint union C 1∪C 2 of a 1-element chain with a 2-element chain shows that the bound 1/3 cannot be further increased. In this paper the extreme case is characterized: If P is a poset of width 2 then the bound 1/3 is exact iff P is an ordinal sum of C 1∪C 2's and C 1's.
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Communicated by P. Hell
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Aigner, M. A note on merging. Order 2, 257–264 (1985). https://doi.org/10.1007/BF00333131
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DOI: https://doi.org/10.1007/BF00333131