A NUMERICAL NOTE ON UPPER BOUNDS FOR B 2 [g] SETS

Abstract : Sidon sets are those sets such that the sums of two of its elements never coincide. They go back to the 30s 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 B 2 [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, are 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 B 2 [g] set in an interval of integers in the cases g = 2, 3, 4 and 5.
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  • HAL Id : hal-01361725, version 3
  • ARXIV : 1609.02771

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Laurent Habsieger, Alain Plagne. A NUMERICAL NOTE ON UPPER BOUNDS FOR B 2 [g] SETS. Experimental Mathematics, Taylor & Francis, 2018, 27 (2), pp.208-214. ⟨hal-01361725v3⟩

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