On the average size of sets in intersecting Sperner families (Q1850012)

\textit{D. J. Kleitman} and \textit{E. C. Milner} [Discrete Math. 6, 141-147 (1973; Zbl 0267.05001)] showed that on an \(n\)-element underlying set any Sperner system having at least \({n\choose k}\) elements has average set-size of at least \(k.\) The result has several generalizations. This paper started to study the same problem on intersecting Sperner families. The main result of the paper shows the analogous result on the average size of intersecting Sperner families assuming that \(k \leq (n+2)/2- \sqrt{n} / 2.\) It is also shown that the statement is false in a certain range of \(k.\) The proofs are based on the known description of the convex hull of the intersecting Sperner families.