Abstract

Given X⊆ZN, X is called a cyclic basis if (X+X)∪X=ZN, symmetric if x∈X implies −x∈X, and sum-free if (X+X)∩X=∅. We ask, for which m, N∈Z+ can the set of non-identity elements of ZN be partitioned into m symmetric sum-free cyclic bases? If, in addition, we require that distinct cyclic bases interact in a certain way, we get a proper relation algebra called a Ramsey algebra. Ramsey algebras (which have also been called Monk algebras) have been constructed previously for 2≤m≤7. In this manuscript, we provide constructions of Ramsey algebras for every positive integer m with 2≤m≤400, with the exception of m=8 and m=13.

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