Open AccessExistence conditions for k- barycentric Olson constant
Author(s) -
Luz Elimar Marchan,
Óscar Ordaz,
Felicia Villaroel,
José Antonio Domínguez Salazar
Publication year - 2020
Publication title -
revista de matemáticas
Language(s) - English
Resource type - Journals
eISSN - 2215-3373
pISSN - 1409-2433
DOI - 10.15517/rmta.v28i1.33773
Subject(s) - mathematics , integer (computer science) , combinatorics , barycentric coordinate system , abelian group , constant (computer programming) , group (periodic table) , physics , geometry , quantum mechanics , computer science , programming language
Let (G, +) be a finite abelian group and 3 ≤ k ≤ |G| a positive integer. The k-barycentric Olson constant denoted by BO(k, G) is defined as the smallest integer ℓ such that each set A of G with |A| = ℓ contains a subset with k elements {a1, . . . , ak} satisfying a1 + · · · + ak = kaj for some 1 ≤ j ≤ k. We establish some general conditions on G assuring the existence of BO(k, G) for each 3 ≤ k ≤ |G|. In particular, from our results we can derive the existence conditions for cyclic groups and for elementary p-groups p ≥ 3. We give a special treatment over the existence condition for the elementary 2-groups.