Some correlation inequalities in finite posets (Q1076047)

A new type of correlation of the posets \({\mathcal A}\) and \({\mathcal B}\) with respect to another poset \({\mathcal R}\) is studied. All posets are defined on \({\mathcal X}\). The correlation is presented by some inequalities. It is proved that well-known correlation inequalities, the \(xyz\) inequality and an inequality of Graham, Yao and Yao, can be considered as giving cases when this correlation holds. Main result is a classification of all \({\mathcal R}\) such that the correlation relation holds for all pairs of elements of \({\mathcal X}\).