Elsevier

Discrete Mathematics

Volume 257, Issues 2–3, 28 November 2002, Pages 311-327
Discrete Mathematics

A combinatorial approach to correlation inequalities

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Abstract

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.

Keywords

Partially ordered set
Correlation

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Research supported in part by the National Science Foundation.