Cross-sperner families

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

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)44-51
Number of pages8
JournalStudia Scientiarum Mathematicarum Hungarica
Volume49
Issue number1
DOIs
StatePublished - Mar 1 2012

Keywords

  • Extremal set systems
  • Primary 05D05
  • Sperner property

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