On the average size of sets in intersecting Sperner families Original Research Article

We show that the average size of subsets of [n] forming an intersecting Sperner family of cardinality not less than (n−1k−1) is at least k provided that k⩽n/2−n/2+1. The statement is not true if n/2⩾k>n/2−8n+1/8+9/8.