Abstract
For a finite partially ordered set (poset) P, denote by p(x<y) the fraction of linear extensions of P in which x precedes y. It is shown that if p(x<y) and p(y<z) are each at least u with u≥ρ≈0.78, then p(x<z) is at least u. The result stated is mainly a consequence of the XYZ inequality [5] and a theorem of Keith Ball (1988) which allows us to reduce to a 2-dimensional version of the problem.
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Yu, Y. On Proportional Transitivity of Ordered Sets. Order 15, 87–95 (1998). https://doi.org/10.1023/A:1006086010382
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DOI: https://doi.org/10.1023/A:1006086010382