论文信息 - A combinatorial approach to correlation inequalities

A combinatorial approach to correlation inequalities

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.

William T. Trotter | Graham R. Brightwell | G. Brightwell | W. T. Trotter

[1] L. Shepp. The XYZ Conjecture and the FKG Inequality , 1982 .

[2] Lawrence A. Shepp,et al. The FKG Inequality and Some Monotonicity Properties of Partial Orders , 1980, SIAM J. Algebraic Discret. Methods.

[3] Andrew Chi-Chih Yao,et al. Some Monotonicity Properties of Partial Orders , 1979, SIAM J. Algebraic Discret. Methods.

[4] D. E. Daykin,et al. An inequality for the weights of two families of sets, their unions and intersections , 1978 .

[5] Richard P. Stanley,et al. Two Combinatorial Applications of the Aleksandrov-Fenchel Inequalities , 1981, J. Comb. Theory, Ser. A.

[6] D. E. Daykin,et al. Order Preserving Maps and Linear Extensions of a Finite Poset , 1985 .

[7] P. Fishburn. A correlational inequality for linear extensions of a poset , 1984 .