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 extentions 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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