Families of finite sets with minimum shadows

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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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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AMS subject classification (1980)

  • 05 C 35