Aequationes mathematicae

, Volume 78, Issue 1, pp 101-112

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

  • E. L. Monte CarmeloAffiliated withDepartamento de Matemática, Universidade Estadual de Maringá Email author 
  • , C. F. X. de Mendonça NetoAffiliated withEscola de Artes, Ciências e Humanidades, Universidade de São Paulo

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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 11H71 secondary 11B75, 94B75


Short coverings extremal problems sum-free sets cyclic groups