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The number of B h ‐sets of a given cardinality
Author(s) -
Dellamonica Domingos,
Kohayakawa Yoshiharu,
Lee Sang June,
Rödl Vojtěch,
Samotij Wojciech
Publication year - 2018
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12082
Subject(s) - mathematics , cardinality (data modeling) , cardinal number (linguistics) , combinatorics , discrete mathematics , computer science , data mining , linguistics , philosophy
For any integer h ⩾ 2 , a set A of integers is called a B h ‐ set if all sumsa 1 + ⋯ + a h , witha 1 , … , a h ∈ A anda 1 ⩽ ⋯ ⩽ a h , are distinct. We obtain essentially sharp asymptotic bounds for the number of B h ‐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 B h ‐set contained in a typical m ‐element subset of { 1 , … , n } .