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Original Articles

A Numerical Note on Upper Bounds for B2[g] Sets

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ABSTRACT

Sidon sets are those sets such that the sums of two of its elements never coincide. They go back to the 1930s when Sidon asked for the maximal size of a subset of consecutive integers with that property. This question is now answered in a satisfactory way. Their natural generalization, called B2[g] sets and defined by the fact that there are at most g ways (up to reordering the summands) to represent a given integer as a sum of two elements of the set, is much more difficult to handle and not as well understood. In this article, using a numerical approach, we improve the best upper estimates on the size of a B2[g] set in an interval of integers in the cases g = 2, 3, 4, and 5.

2000 AMS Subject Classification:

Additional information

Funding

Both authors are supported by the ANR grant Cæsar, number ANR 12 - BS01 - 0011.

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