caa a22 4500 475807642 CHVBK 20180406123751.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1023/A:1008367006853 doi (NATIONALLICENCE)springer-10.1023/A:1008367006853 Bajnok Béla Department of Mathematics, Gettysburg College, 17325-1486, Gettysburg, PA, USA aut Spherical Designs and Generalized Sum-Free Sets in Abelian Groups [Elektronische Daten] [Béla Bajnok] 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. Kluwer Academic Publishers, 2000 Spherical design nationallicence sum-free set nationallicence sidon-set nationallicence Designs, Codes and Cryptography Kluwer Academic Publishers 21/1-3(2000-10-01), 11-18 0925-1022 21:1-3<11 2000 21 10623 https://doi.org/10.1023/A:1008367006853 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008367006853 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bajnok Béla Department of Mathematics, Gettysburg College, 17325-1486, Gettysburg, PA, USA aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 21/1-3(2000-10-01), 11-18 0925-1022 21:1-3<11 2000 21 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer