Chen, Sheng On Sidon sequences of even orders. (English) Zbl 0781.11010 Acta Arith. 64, No. 4, 325-330 (1993). Let \(h\geq 2\) be an integer. A set of positive integers \(A\) is called a \(B_ h\)-sequence, or a Sidon sequence of order \(h\), if all sums \(a_ 1+a_ 2+ \cdots+a_ h\), where \(a_ i\in B\) (\(i=1,2,\dots,h\)), are distinct up to rearrangements of the summands. Let \(A(n)\) be the cardinality of the set \(A\cap [0,n]\). It is proved that, for any \(B_{2k}\)-sequence \(A\), \[ \liminf_{n\to\infty} A(n) \root 2k \of {{{\log n} \over n}}<\infty, \] which extends the results of P. Erdős (k=1) and J. C. M. Nash (k=2) [Can. Math. Bull. 32, 446-449 (1989; Zbl 0692.10046)] and improves the results of others. Reviewer: S.Chen (San Marcos/TX) Cited in 1 ReviewCited in 1 Document MSC: 11B83 Special sequences and polynomials 11B50 Sequences (mod \(m\)) 05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) Keywords:difference sets; \(B_ h\)-sequence; Sidon sequence of order \(h\); cardinality Citations:Zbl 0692.10046 PDFBibTeX XMLCite \textit{S. Chen}, Acta Arith. 64, No. 4, 325--330 (1993; Zbl 0781.11010) Full Text: DOI EuDML