ON FINITE ADDITIVE 2-BASES

Laurent Habsieger (1)

1 CTN - Combinatoire, théorie des nombres

For a positive integer N , a set B of integers from {0, 1,. .. , N − 1} is called an additive 2-basis for N if every integer n ∈ {0, 1,. .. , N − 1} may be represented as the sum of 2 elements of B. We discuss the methods used to estimate the minimal size of an additive 2-basis for N. We provide new examples to enrich this survey, which give good bounds. For instance, we slightly improve on the current record, from 0.46972 to 0.46906.

Domaines: Théorie des nombres [math.NT]

Laurent Habsieger. ON FINITE ADDITIVE 2-BASES. Transactions of the American Mathematical Society, 2014, 366 (12), pp.6629-6646. ⟨hal-02072709⟩