TY - JOUR

T1 - Cross-sperner families

AU - Gerbner, Dániel

AU - Lemons, Nathan

AU - Palmer, Cory

AU - Patkós, Balázs

AU - Szécsi, Vajk

PY - 2012/3/1

Y1 - 2012/3/1

N2 - 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.

AB - 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.

KW - Extremal set systems

KW - Primary 05D05

KW - Sperner property

UR - http://www.scopus.com/inward/record.url?scp=84858221340&partnerID=8YFLogxK

U2 - 10.1556/SScMath.2011.1185

DO - 10.1556/SScMath.2011.1185

M3 - Article

AN - SCOPUS:84858221340

SN - 0081-6906

VL - 49

SP - 44

EP - 51

JO - Studia Scientiarum Mathematicarum Hungarica

JF - Studia Scientiarum Mathematicarum Hungarica

IS - 1

ER -