6533b829fe1ef96bd128a3a4

RESEARCH PRODUCT

Thin bases of order h

Valentin Blomer

subject

Discrete mathematicsCombinatoricsClass (set theory)Algebra and Number TheoryIntegerOrder (group theory)Value (computer science)Basis (universal algebra)MathematicsAnsatz

description

Abstract A subset A⊆ N 0 is called a basis of order h if every positive integer can be represented as a sum of h members of A . Thin bases of order h will be constructed in this paper, for each h ⩾2, where the value of lim sup A(n)/ n h is smaller than that of thin bases known so far. In the most important case h =2 it is shown that for the considered class of bases (which generalizes an ansatz of Stohr) the result is best possible up to an e >0.

10.1016/s0022-314x(02)00036-7http://dx.doi.org/10.1016/s0022-314x(02)00036-7