Abstract
A subset S of an additive group G is said to be a sum-free set if S ∩ (S + S) = Ø. A sum-free set S is said to be locally maximal if for every sum-free set T such that S⊑T⊑G, we have S = T.
Here we determine some sum-free cyclotomic classes in finite fields and from them, we construct new supplementary difference sets, association schemes and block designs. We also continue our study of locally maximal sum-free sets in groups of small orders and in finite fields.
Supported in part by U.S. A.E.C., contract number AT(11-1)-3077-V, at the Courant Institute of Mathematical Sciences, New York University.
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References
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© 1974 Springer-Verlag
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Street, A.P., Whitehead, E.G. (1974). Sum-free sets, difference sets and cyclotomy. In: Holton, D.A. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0057384
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DOI: https://doi.org/10.1007/BFb0057384
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