On the average size of sets in intersecting Sperner families

We show that the average size of subsets of [n] forming an intersecting Sperner family of cardinality not less than ((n-1)(k-1)) is at least k provided that k less than or equal to n/2 – rootn/2 + 1. The statement is not true if n/2 greater than or equal to k > n/2 – root8n+ 1/8 + 9/8. (C) 2002 Elsevier Science B.V. All rights reserved.