Aequationes mathematicae

, 78:101

Extremal problems on sum-free sets and coverings in tridimensional spaces

  • E. L. Monte Carmelo
  • C. F. X. de Mendonça Neto

DOI: 10.1007/s00010-009-2971-0

Cite this article as:
Carmelo, E.L.M. & de Mendonça Neto, C.F.X. Aequat. Math. (2009) 78: 101. doi:10.1007/s00010-009-2971-0


Given a prime power q, define c(q) as the minimum cardinality of a subset H of \({\mathbb{F}}^3_q\) which satisfies the following property: every vector in this space differs in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c(q).

Mathematics Subject Classification (2000).

Primary 11H71secondary 11B75, 94B75


Short coveringsextremal problemssum-free setscyclic groups

Copyright information

© Birkhäuser Verlag, Basel 2009

Authors and Affiliations

  • E. L. Monte Carmelo
    • 1
  • C. F. X. de Mendonça Neto
    • 2
  1. 1.Departamento de MatemáticaUniversidade Estadual de MaringáMaringá, ParanáBrazil
  2. 2.Escola de Artes, Ciências e HumanidadesUniversidade de São PauloSão PauloBrazil