Combinatorica

, Volume 13, Issue 3, pp 269–277

Correlation inequalities and a conjecture for permanents

  • Yosef Rinott
  • Michael Saks
Article

DOI: 10.1007/BF01202353

Cite this article as:
Rinott, Y. & Saks, M. Combinatorica (1993) 13: 269. doi:10.1007/BF01202353

Abstract

This paper presents conditions on nonnegative real valued functionsf1,f2,...,fm andg1,g2,...gm implying an inequality of the type
$$\mathop \Pi \limits_{i = 1}^m \int {f_i (x)d\mu } (x) \leqslant \mathop \Pi \limits_{i = 1}^m \int {g_i (x)d\mu } (x).$$
This “2m-function” theorem generalizes the “4-function” theorem of [2], which in turn generalizes a “2-function” theorem ([8]) and the celebrated FKG inequality. It also contains (and was partly inspired by) an “m against 2” inequality that was deduced in [5] from a general product theorem.

AMS subject classification code (1991)

60 C 05 60 E 15 06 D 99 05 D 99 06 A 07 

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Yosef Rinott
    • 1
  • Michael Saks
    • 2
    • 3
  1. 1.Department of MathematicsUCSDLa Jolla
  2. 2.Department of MaématicsRutgers UniversityNew Brunswick
  3. 3.Department of Computer Science and EngineeringUCSDLa Jolla

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