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Spherical Designs and Generalized Sum-Free Sets in Abelian Groups

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Abstract

We extend the concepts of sum-freesets and Sidon-sets of combinatorial number theory with the aimto provide explicit constructions for spherical designs. We calla subset S of the (additive) abelian group G t-free if for all non-negative integers kand l with k+l ≤ t, the sum of k(not necessarily distinct) elements of S does notequal the sum of l (not necessarily distinct) elementsof S unless k=l and the two sums containthe same terms. Here we shall give asymptotic bounds for thesize of a largest t-free set in Z n,and for t ≤ 3 discuss how t-freesets in Z n can be used to constructspherical t-designs.

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  1. Department of Mathematics, Gettysburg College, Gettysburg, PA, 17325-1486, USA

    Béla Bajnok

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Bajnok, B. Spherical Designs and Generalized Sum-Free Sets in Abelian Groups. Designs, Codes and Cryptography 21, 11–18 (2000). https://doi.org/10.1023/A:1008367006853

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