On the shadow of squashed families of k-sets

The shadow of a collectionA of k-sets is deflned as the collection of the (ki 1)-sets which are contained in at least one k-set of A.G ivenjAj ,t he size of the shadow is minimum whenA is the family of the flrst k-sets in squashed order (by deflnition, a k-set A is smaller than a k-set B in the squashed order if the largest element of the symmetric difierence ofA and B is inB). We give a tight upper bound and an asymptotic formula for the size of the shadow of squashed families of k-sets.