Let us fix the integers n,k, and r so that n≥k≥r≥1. We consider an n-element set V. We shall call its k- and r-element subsets k-ads and r-ads for brevity. We introduce four functions: F(n,k,r,l) is the largest number of r-ads under the condition that there are no more than l of them in any k-ad. f(n,k,r,l) is the smallest number of r-ads under the condition that there are no fewer than l of them in any k-add. G(n,k,r,l) is the largest number of k-ads under the condition that any r-ad occurs in no more than l of them. g(n,k,r,l) is the smallest number of k-ads under the condition that any r-ad occurs in no fewer than l of them. The aim of this note is to compute the functions F,f,G, and g.
