This web page contains the abstract of my paper:

"A Monotonicity Property of Partial Orders" with D.J. Kleitman, Studies in Applied Mathematics, 65(1981), p. 81-83.

Abstract: A proof using the FKG inequalities of the following result is obtained. Let P be a partially ordered set on a1<=a2<=...<=am and b1<=b2<=...<=bn. Let P(x) be the proportion of linear extensions of P for which x holds. If x and y are disjunctions of conjunctions of additional inequalities of the form ai>=bj, then P(x and y)>=P(x)*P(y). An example is provided that shows the result can be false if we don't assume the {ai} and {bj} are linearly ordered in P.

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