A note on weak Sidon sequences
نویسنده
چکیده
A sequence (ai) of integers is weak Sidon or well-spread if the sums ai + aj , for i < j , are all different. Let f (N) denote the maximum integer n for which there exists a weak Sidon sequence 0 a1< · · ·<an N . Using an idea of Lindström [An inequality for B2-sequences, J. Combin. Theory 6 (1969) 211–212], we offer an alternate proof that f (N)<N1/2 + O(N1/4), an inequality due to Ruzsa [Solving a linear equation in a set of integers I, Acta. Arith. 65 (1993) 259–283]. The present proof improves Ruzsa’s bound by decreasing the implicit constant, essentially from 4 to √ 3. © 2005 Elsevier B.V. All rights reserved.
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عنوان ژورنال:
- Discrete Mathematics
دوره 299 شماره
صفحات -
تاریخ انتشار 2005