UPPER BOUNDS FOR BH[G]-SETS WITH SMALL H

摘要

For g 2 and h 3, we give small improvements on the maximum size of a Bh[g]- set contained in the interval {1, 2, . . . , N}. In particular, we show that a B3[g]-set in {1, 2, . . . , N} has at most (14.3gN)1/3 elements. The previously best known bound was (16gN)1/3 proved by Cilleruelo, Ruzsa, and Trujillo. We also introduce a related optimization problem that may be of independent interest.