Tilted Sperner families

Tilted Sperner families

Let A be a family of subsets of an n-set such that A does not contain distinct sets A and B with |A∖B|=2|B∖A|. How large can A be? Our aim in this note is to determine the maximum size of such an A. This answers a question of Kalai. We also give some related results and conjectures.

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Veröffentlicht in:Discrete Applied Mathematics 2014-01, Vol.163, p.194-198
Hauptverfasser: Leader, Imre, Long, Eoin
Format: Artikel
Sprache:eng
Schlagworte:
Extremal combinatorics
Mathematical analysis
Sperner families
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Zusammenfassung:Let A be a family of subsets of an n-set such that A does not contain distinct sets A and B with |A∖B|=2|B∖A|. How large can A be? Our aim in this note is to determine the maximum size of such an A. This answers a question of Kalai. We also give some related results and conjectures.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2012.02.024