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2024 | OriginalPaper | Chapter

Additive Combinatorics in Groups and Geometric Combinatorics on Spheres

Author : Béla Bajnok

Published in: Combinatorics, Graph Theory and Computing

Publisher: Springer Nature Switzerland

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Abstract

We embark on a tour that takes us through four closely related topics: the dual concepts of independence and spanning in finite abelian groups and the analogous dual concepts of designs and distance sets on spheres. We review some of the main known results in each area, mention several open questions, and discuss some connections among these four interesting topics.

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next chapter A Walk Through Some Newer Parts of Additive Combinatorics

B. Bajnok, Construction of spherical t-designs. Geom. Dedicata, 43 (1992), 167–179.MathSciNetCrossRef

B. Bajnok, Constructions of spherical 3-designs. Graphs Combin., 14:2 (1998), 97–107.MathSciNetCrossRef

B. Bajnok, The spanning number and the independence number of a subset of an abelian group. In Number theory (New York, 2003), Springer, New York, 2004, 1–16.

B. Bajnok, Additive Combinatorics: A Menu of Research Problems. CRC Press, Boca Raton, 2018, xix+390 pp.

B. Bajnok and I. Ruzsa, The independence number of a subset of an abelian group. Integers, 3 (2003), Paper A2.

E. Bannai, On extremal finite sets in the sphere and other metric spaces. London Math. Soc. Lecture Note Ser., 131 (1988), 13–38.MathSciNet

E. Bannai and R. M. Damerell, Tight spherical designs I. J. Math. Soc. Japan, 31 (1979), 199–207.MathSciNetCrossRef

E. Bannai and R. M. Damerell. Tight spherical designs II. J. London Math. Soc. (2), 21 (1980), 13–30.MathSciNetCrossRef

S. Boumova, P. Boyvalenkov, and D. Danev, New nonexistence results for spherical designs. In B. Bojanov, editor, Constructive Theory of Functions, Varna, 2002, 225–232.

10.

P. Boyvalenkov and M. Stoyanova, New nonexistence results for spherical designs. Adv. Math. Commun.7 (2013), no. 3, 279–292.MathSciNetCrossRef

11.

P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs. Geom. Dedicata, 6 (1977), 363–388.MathSciNetCrossRef

12.

C. D. Godsil, Algebraic Combinatorics. Chapman and Hall, New York, 1993, xvi+362 pp.

13.

J. M. Goethals and J. J. Seidel, Spherical designs. Proc. Sympos. Pure Math., 34 (1979), 255–272.MathSciNetCrossRef

14.

R. H. Hardin and N. J. A. Sloane, McLaren’s improved snub cube and other new spherical designs in three dimensions. Discrete Comput. Geom., 15 (1996), 429–441.MathSciNetCrossRef

15.

S. G. Hoggar, Spherical t-designs. In C. J. Colbourn and J. H. Dinitz, editors, The CRC handbook of combinatorial designs, CRC Press, Boca Raton, 1996, 462–466.

16.

M. Kneser, Abschätzungen der asymptotichen Dichte von Summenmengen. Math. Z.58 (1953), 459–484.MathSciNetCrossRef

17.

M. B. Nathanson, Additive Number Theory: Inverse Problems and the Geometry of Sumsets. Springer-Verlag, New York, 1996, xiv+293 pp.

18.

O. R. Musin, Spherical two-distance sets. J. Combin. Theory Ser. A116 (2009), no. 4, 988–995.MathSciNetCrossRef

19.

B. Reznick, Sums of even powers of real linear forms. Mem. Amer. Math. Soc., 463, 1992.

20.

J. J. Seidel, Designs and approximation. Contemp. Math., 111 (1990), 179–186.MathSciNetCrossRef

21.

P. D. Seymour and T. Zaslavsky, Averaging sets: A generalization of mean values and spherical designs. Adv. Math., 52 (1984), 213–240.MathSciNetCrossRef

Title: Additive Combinatorics in Groups and Geometric Combinatorics on Spheres
Author: Béla Bajnok
Publisher: Springer Nature Switzerland
Book: Combinatorics, Graph Theory and Computing
Print ISBN: 978-3-031-62165-9

Electronic ISBN: 978-3-031-62166-6

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-62166-6_1

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