Cross-sperner families

Dániel Gerbner; Nathan Lemons; Cory Palmer; Balázs Patkós; Vajk Szécsi

doi:10.1556/SScMath.2011.1185

Cross-sperner families

Dániel Gerbner, Nathan Lemons, Cory Palmer, Balázs Patkós, Vajk Szécsi

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A pair of families (F, G) is said to be cross-Sperner if there exists no pair of sets F F, G G with F G or G F. There are two ways to measure the size of the pair (F, G): with the sum |F| + |G| or with the product |F| • |G|. We show that if F, G 2[n], then |F| |G| 22n-4 and |F| + |G| is maximal if F or G consists of exactly one set of size 2 provided the size of the ground set n is large enough and both F and G are nonempty.

Original language	English
Pages (from-to)	44-51
Number of pages	8
Journal	Studia Scientiarum Mathematicarum Hungarica
Volume	49
Issue number	1
DOIs	https://doi.org/10.1556/SScMath.2011.1185
State	Published - Mar 1 2012

Keywords

Extremal set systems
Primary 05D05
Sperner property

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10.1556/SScMath.2011.1185

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AU - Lemons, Nathan

AU - Palmer, Cory

AU - Patkós, Balázs

AU - Szécsi, Vajk

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Cross-sperner families

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Keywords

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