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On the Shadow of Squashed Families of K-Sets
The shadow of a collection A of k-sets is defined as the collection of the (k - 1)-sets which are contained in at least one k-set of A. Given jAj, the size of the shadow is minimum when A is the family of the first k-sets in squashed order (by definition, a k-set A is smaller than a k-set B in the squashed order if the largest element of the symmetric difference of A and B is in B). We give a tight upper bound and an asymptotic formula for the size of the shadow of squashed families of k-sets