Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-99-10

October 1999

A Combinatorial Approach to Correlation Inequalities

Graham R. Brightwell and William T. Trotter


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 P.C. Fishburn. We also use our method to give a new proof of a related correlation result of L.A. 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.

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