Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-08T08:21:16.097Z Has data issue: false hasContentIssue false

Reimer's Inequality on a Finite Distributive Lattice

Published online by Cambridge University Press:  11 June 2013

CLIFFORD SMYTH*
Affiliation:
Mathematics and Statistics Department, University of North Carolina Greensboro, Greensboro, NC 27412, USA (e-mail: [email protected])

Abstract

We generalize Reimer's Inequality [6] (a.k.a. the BKR Inequality or the van den Berg–Kesten Conjecture [1]) to the setting of finite distributive lattices.

Keywords

Type
Paper
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]van den Berg, J. and Kesten, H. (1985) Inequalities with applications to percolation and reliability. J. Appl. Probab. 22 556569.Google Scholar
[2]Fortuin, C. M., Kasteleyn, P. W. and Ginibre, J. (1971) Correlation inequalities on some partially ordered sets. Comm. Math. Phys. 22 89103.Google Scholar
[3]Grätzer, G. (2003) General Lattice Theory, Birkhäuser. Reprint of the 1998 second edition.Google Scholar
[4]Harris, T. E. (1960) A lower bound for the critical probability in a certain percolation process. Proc. Cambridge Philos. Soc. 56 1320.Google Scholar
[5]Kleitman, D. J. (1966) Families of non-disjoint subsets. J. Combin. Theory 1 153155.Google Scholar
[6]Reimer, D. (2000) Proof of the van den Berg–Kesten conjecture. Combin. Probab. Comput. 9 2732.Google Scholar