Families of finite sets with minimum shadows
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.