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Sharpening the LYM inequality

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Abstract

The level sequence of a Sperner familyF is the sequencef(F)={f i (F)}, wheref i (F) is the number ofi element sets ofF . TheLYM inequality gives a necessary condition for an integer sequence to be the level sequence of a Sperner family on ann element set. Here we present an indexed family of inequalities that sharpen theLYM inequality.

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Authors and Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, Budapest

    Péter L. Erdős

  2. Institute of Operations Research, University of Bonn, Bonn, Germany

    Péter L. Erdős

  3. Massachusetts Institute of Technology, 02139, Cambridge, MA, U.S.A.

    D. J. Kleitman

  4. Eötvös University, Budapest

    L. A. Székely

  5. University of New Mexico, Albuquerque

    L. A. Székely

  6. University of Paris VII, 2 Place Jussieu, 75005, Paris, France

    P. Frankl

  7. University of California, San Diego

    M. E. Saks

Authors
  1. Péter L. Erdős
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  2. P. Frankl
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  3. D. J. Kleitman
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  4. M. E. Saks
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  5. L. A. Székely
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Additional information

Research supported in part by Alexander v. Humboldt-Stiftung

Research supported in part by NSF under grant DMS-86-06225 and AFOSR grant OSR-86-0078

Research supported in part by NSF grant CCR-8911388

Research supported in part by OTKA 327 0113

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Erdős, P.L., Frankl, P., Kleitman, D.J. et al. Sharpening the LYM inequality. Combinatorica 12, 287–293 (1992). https://doi.org/10.1007/BF01285817

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  • DOI: https://doi.org/10.1007/BF01285817

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