Upper and lower bounds for finite Bh[g] sequences

Javier Cilleruelo, Imre Z. Ruzsa, Carlos Trujillo

Research output: Contribution to journalArticle

15 Citations (Scopus)


We give a non-trivial upper bound for Fh(g, N), the size of a Bh,[g] subset of 1,...N, when g > 1. In particular, we prove F2(g, N) ≤ 1.864(gN)1/2 + 1, and Fh, (g, N) ≤ (hh!gN)1/h, h > 2. On the other hand, we exhibit B2[g] subsets of {1,...N} with elements.

Original languageEnglish
Pages (from-to)26-34
Number of pages9
JournalJournal of Number Theory
Issue number1
Publication statusPublished - Nov 1 2002

ASJC Scopus subject areas

  • Algebra and Number Theory

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