Spherical Designs and Generalized Sum-Free Sets in Abelian Groups |
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Authors: | Béla Bajnok |
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Institution: | (1) Department of Mathematics, Gettysburg College, Gettysburg, PA 17325-1486, USA |
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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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Keywords: | Spherical design sum-free set sidon-set |
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