On the average size of sets in intersecting sperner families

Authors:
Christian Bey;Konrad Engel;Gyula O. H. Katona;Uwe Leck
Affiliations:
Fachbereich Mathematik, Universitat Rostock, 18051 Rostock, Germany;Fachbereich Mathematik, Universitat Rostock, 18051 Rostock, Germany;Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, Budapest 1364, Hungary;Fachbereich Mathematik, Universitat Rostock, 18051 Rostock, Germany
Venue:
Discrete Mathematics - Kleitman and combinatorics: a celebration
Year:
2002

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Abstract

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.