TY - JOUR

T1 - The number of B h -sets of a given cardinality:

AU - Dellamonica, Domingos

AU - Kohayakawa, Yoshiharu

AU - Lee, Sang June

AU - Rödl, Vojtěch

AU - Samotij, Wojciech

N1 - Publisher Copyright: © 2017 London Mathematical Society.

PY - 2018/3

Y1 - 2018/3

N2 - For any integer h≥2, a set A of integers is called a Bh-set if all sums a1+⋯+ah, with a1,⋯,ahϵA and a1≤⋯≤ah, are distinct. We obtain essentially sharp asymptotic bounds for the number of Bh-sets of a given cardinality that are contained in the interval {1,⋯,n}. As a consequence of these bounds, we determine, for any integer m≤n, the cardinality of the largest Bh-set contained in a typical m-element subset of {1,⋯,n}.

AB - For any integer h≥2, a set A of integers is called a Bh-set if all sums a1+⋯+ah, with a1,⋯,ahϵA and a1≤⋯≤ah, are distinct. We obtain essentially sharp asymptotic bounds for the number of Bh-sets of a given cardinality that are contained in the interval {1,⋯,n}. As a consequence of these bounds, we determine, for any integer m≤n, the cardinality of the largest Bh-set contained in a typical m-element subset of {1,⋯,n}.

UR - http://www.scopus.com/inward/record.url?scp=85037992383&partnerID=8YFLogxK

U2 - https://doi.org/10.1112/plms.12082

DO - https://doi.org/10.1112/plms.12082

M3 - مقالة

SN - 0024-6115

VL - 116

SP - 629

EP - 669

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 3

ER -