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Harmonics and Combinatorics

  • J. J. Seidel
Part of the Mathematics and Its Applications book series (MAIA, volume 18)

Abstract

The geometry of the sphere in Rd, which provides a setting for various combinatorial configurations, is governed by spherical harmonics. Bounds for the cardinality of such configurations may be derived by use of a linear programming method. This applies to equiangular lines, root systems, and Newton numbers. The methods may be extended to the hyperbolic case, as well as to the discrete case. The present paper aims to survey these harmonic methods and some of their results. The paper does not consider complex, quaternionic, octave, and other more general situations, which for instance appear in [5] and [8].

Keywords

Spherical Harmonic Cubature Formula Harmonic Polynomial Addition Formula Linear Programming Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© D. Reidel Publishing Company 1984

Authors and Affiliations

  • J. J. Seidel

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