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Families of finite sets with minimum shadows

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Abstract

The following problem was answered by a theorem of Kruskal, Katona, and Lindström about 20 years ago: Given a family ofk-element sets ℱ, |ℱ|=m, at least how many (k-d)-element subsets are contained in the members of ℱ? This paper deals with the extremal families, e.g., they are completely described for infinitely many values ofm.

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Author notes

  1. J. R. Griggs

    Present address: Dept. Math. Stat., Univ. South Carolina, 29208, Columbia, SC, U.S.A.

Authors and Affiliations

  1. Math. Inst. Hungarian Acad. Sci., P.O.B. 127, 1364, Budapest, Hungary

    Z. Füredi

  2. Department of Mathematics, University of Southern California, 90089-1113, Los Angeles, California, U.S.A.

    J. R. Griggs

Authors
  1. Z. Füredi
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  2. J. R. Griggs
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Additional information

Research of second author supported in part by the National Science Foundation.

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Füredi, Z., Griggs, J.R. Families of finite sets with minimum shadows. Combinatorica 6, 355–363 (1986). https://doi.org/10.1007/BF02579261

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  • DOI: https://doi.org/10.1007/BF02579261

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