Events correlated with respect to every subposet of a fixed poset
Posets A, B of \(X\times X\) are said to be correlated to a third poset R on X if P(A/R)\(\leq P(A/R\cup B)\). Here P(C/R) is the probability that a randomly chosen linear extension on R is also a linear extension of C. The author classifies posets R on X such that for all subposets S of R and all distinct elements x, y, u, v of X, (x,y) is correlated to (u,v) of S. A discussion about a correlation inequality appears also in the paper.
scientific article; zbMATH DE number 4160797
scientific article