Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 141-144 |
| Number of pages | 4 |
| Journal | Discrete Mathematics |
| Volume | 299 |
| Issue number | 1-3 |
| DOIs | |
| State | Published - Aug 28 2005 |
Keywords
- Weak Sidon
- Well-spread