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 -