A combinatorial approach to correlation inequalities
Brightwell, G.
& Trotter, W. T.
(2002).
A combinatorial approach to correlation inequalities.
Discrete Mathematics,
257(2-3), 311-327.
https://doi.org/10.1016/S0012-365X(02)00432-6
& Trotter, W. T.
(2002).
A combinatorial approach to correlation inequalities.
Discrete Mathematics,
257(2-3), 311-327.
https://doi.org/10.1016/S0012-365X(02)00432-6
In this paper, we initiate a combinatorial approach to proving correlation inequalities for finite partially ordered sets. A new proof is provided for the strong form of the XYZ theorem, due to Fishburn. We also use our method to give a new proof of a related correlation result of Shepp involving two sets of relations. Our arguments are entirely combinatorial in the sense that they do not make use of the Ahlswede/Daykin theorem or any of its relatives.