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Article

Reimer's Inequality on a Finite Distributive Lattice

  • CLIFFORD SMYTH (a1)
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.

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COPYRIGHT: © Cambridge University Press 2013 
References
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[1]van den Berg, J. and Kesten, H. (1985) Inequalities with applications to percolation and reliability. J. Appl. Probab. 22 556–569.
[2]Fortuin, C. M., Kasteleyn, P. W. and Ginibre, J. (1971) Correlation inequalities on some partially ordered sets. Comm. Math. Phys. 22 89–103.
[3]Grätzer, G. (2003) General Lattice Theory, Birkhäuser. Reprint of the 1998 second edition.
[4]Harris, T. E. (1960) A lower bound for the critical probability in a certain percolation process. Proc. Cambridge Philos. Soc. 56 13–20.
[5]Kleitman, D. J. (1966) Families of non-disjoint subsets. J. Combin. Theory 1 153–155.
[6]Reimer, D. (2000) Proof of the van den Berg–Kesten conjecture. Combin. Probab. Comput. 9 27–32.
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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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