Abstract

ERAZO, IRENE; LOPEZ, JOHN  and  TRUJILLO, CARLOS. A combinatorial problem that arose in integer B ₃ Sets. Rev.colomb.mat. [online]. 2019, vol.53, n.2, pp.195-203.  Epub Mar 20, 2020. ISSN 0034-7426.

Let A = {α 1 , α 2 ,... , α k } be a set of positive integers with k ≥ 3, such that α 1 ≤ α 2 ≤ α 3 ≤ … ≤ α k = N. Our problem is to investigate the number of triplets (α r , α s , α t ) Є A3 with a r < a s < a t , satisfying

α r + α s - α t < 0 and - α r + α s + α t > N. (1)

In this paper we give an upper bound for the maximum number of such a triplets in an arbitrary set of integers with k elements. We also find the number of triplets satisfying () for some families of sets in order to determine lower bounds for the maximum number of such a triplets that a set with k elements can have.

Keywords : B ₃ sets; Sidon sets.

        · abstract in Spanish     · text in English     · English ( pdf )