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The Ahlswede-Daykin Theorem

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Numbers, Information and Complexity

Abstract

In 1978, Rudolf Ahlswede and David Daykin published a theorem which says that a certain inequality on nonnegative real valued functions for pairs of points in a finite distributive lattice extends additively to pairs of lattice subsets. It is an elegant theorem with widespread applications to inequalities for systems of subsets, linear extensions of partially ordered sets, and probabilistic correlation. We review the theorem and its applications, and describe a recent generalization to n-tuples of points and subsets in distributive lattices. Although many implications of the Ahlswede-Daykin theorem follow from the weaker hypotheses of the widely-cited FKG theorem, several important implications are noted to require the stronger hypotheses of the basic theorem of Ahlswede and Daykin.

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Author information

Authors and Affiliations

  1. AT&T Labs-Research, Florham Park, NJ, 07932, USA

    Peter C. Fishburn

  2. Rutgers University, Piscataway, NJ, 08855, USA

    Lawrence A. Shepp

Authors
  1. Peter C. Fishburn
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  2. Lawrence A. Shepp
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Editor information

Editors and Affiliations

  1. Friedrich Schiller-Universität Jena, Germany

    Ingo Althöfer

  2. National University of Singapore, Singapore

    Ning Cai

  3. IBM Germany, Germany

    Gunter Dueck

  4. Universität Bielefeld, Germany

    Levon Khachatrian

  5. Russian Academy of Sciences, Russia

    Mark S. Pinsker

  6. Eötvös Lorand University, Hungary

    Andras Sárközy

  7. Universität Dortmund, Germany

    Ingo Wegener

  8. University of Southern California, Los Angeles, USA

    Zhen Zhang

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© 2000 Springer Science+Business Media New York

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Fishburn, P.C., Shepp, L.A. (2000). The Ahlswede-Daykin Theorem. In: Althöfer, I., et al. Numbers, Information and Complexity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6048-4_41

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  • DOI: https://doi.org/10.1007/978-1-4757-6048-4_41

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4967-7

  • Online ISBN: 978-1-4757-6048-4

  • eBook Packages: Springer Book Archive

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