On barycentric constants

• Florian Luca ^[1] ; Oscar Ordaz ^[2] ; María Teresa Varela ^[3]
  1. [1] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
  2. [2] Universidad Central de Venezuela

     Universidad Central de Venezuela

     Venezuela

     
  3. [3] Universidad Simón Bolívar

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• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 53, Nº. 2, 2012, págs. 1-12
• Idioma: inglés
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• Resumen

  • Let G be an abelian group with n elements. Let S be a sequence of elements of G, where the repetition of elements is allowed. Let |S| be the cardinality, or the length of S. A sequence S ⊆ G with |S| ≥ 2 is barycentric or has a barycentric-sum if it contains one element aj such that Σai ∈ Sai = |S|aj. This paper is a survey on the following three barycentric constants: the k-barycentric Olson constant BO(k, G), which is the minimum positive integer t ≥ k ≥ 3 such that any subset of t elements of G contains a barycentric subset with k elements, provided such an integer exists; the k-barycentric Davenport constant BD(k, G), which is the minimum positive integer t such that any subsequence of t elements of G contains a barycentric subsequence with k terms; the barycentric Davenport constant BD(G), which is the minimum positive integer t ≥ 3 such that any subset of t elements of G contains a barycentric subset. New values and bounds on the above barycentric constants when G = Zn is the group of integers modulo n are also given.