On the ubiquity of Sidon sets
نویسنده
چکیده
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 B2[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 B2[g]-sets, in the sense that if B2[g](k, n) denotes the number of B2[g]-sets of cardinality k contained in the interval {1, 2, . . . , n}, then limn→∞ B2[g](k, n)/ ( n k )
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