Open AccessA combinatorial problem that arose in integer B3 Sets
Author(s) -
Irene Erazo,
John D. López,
Carlos Trujillo
Publication year - 2019
Publication title -
revista colombiana de matemáticas/revista colombiana de matematicas
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.176
H-Index - 7
eISSN - 2357-4100
pISSN - 0034-7426
DOI - 10.15446/recolma.v53n2.85538
Subject(s) - combinatorics , integer (computer science) , mathematics , set (abstract data type) , upper and lower bounds , order (exchange) , discrete mathematics , computer science , programming language , mathematical analysis , finance , economics
Let A = {a1, a2, …, ak} be a set of positive integers with k ≥ 3,such that a1 ≤ a2 ≤ a3 … ak = N. Our problem is to investigate thenumber of triplets (ar, as, at) ∈ A3 with ar N.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.