Abstract :
A setEof integers is called aBh[g] set if every integer can be written in at mostgdifferent ways as a sum ofhelements ofE. We give an upper bound for the size of aBh[1] subset {n1, …,nk} of {1, …,n} wheneverh=2mis an even integer:[formula]For the caseh=2 (h=4) this has already been proved by Erdimages and Turán (by Lindström). It has been independently proved for all evenhby Jia [9] who used an elementary combinatorial argument. Our method uses a result, which we prove, related to the minimum of dense cosine sums which roughly states that if 1less-than-or-equals, slantλ1<…<λNless-than-or-equals, slant(2−var epsilon) NareNdifferent integers then[formula]Finally we exhibit some dense finite and infiniteB2[2] sequences.
