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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https://hal.archives-ouvertes.fr/hal-01361725
Contributor : Laurent Habsieger <>
Submitted on : Tuesday, September 27, 2016 - 4:05:56 PM
Last modification on : Wednesday, March 27, 2019 - 4:10:22 PM
Document(s) archivé(s) le : Wednesday, December 28, 2016 - 12:22:57 PM

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  • HAL Id : hal-01361725, version 2
  • ARXIV : 1609.02771

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Laurent Habsieger, Alain Plagne. A NUMERICAL NOTE ON UPPER BOUNDS FOR B 2 [g] SETS. 2016. ⟨hal-01361725v2⟩

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