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

Domingos Dellamonica, Yoshiharu Kohayakawa, Sang June Lee, Vojtěch Rödl, Wojciech Samotij

Research output: Contribution to journalArticlepeer-review


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}.

Original languageEnglish
Pages (from-to)629-669
Number of pages41
JournalProceedings of the London Mathematical Society
Issue number3
StatePublished - Mar 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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