A Sidon set is a set A of integers such that no integer has two essentially distinct representations as the sum of two elements of A. More generally, for every positive integer g, a B_2[g]-set is a set A of integers such that no integer has more than g essentially distinct representations as the sum of two elements of A. It is proved that almost all small sumsets of {1,2,...,n} are B_2[g]-sets, in the sense that if B_2[g](k,n) denotes the number of B_2[g]-sets of cardinality k contained in the interval {1,2,...,n}, then lim_{n\to\infty} B_2[g](k,n)/\binom{n}{k} = 1 if k = o(n^{g/(2g+2)}).
CITATION STYLE
Nathanson, M. B. (2004). On the ubiquity of Sidon sets. In Number Theory (pp. 263–272). Springer New York. https://doi.org/10.1007/978-1-4419-9060-0_16
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