Harmonics and Combinatorics
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  and .
KeywordsSpherical Harmonic Cubature Formula Harmonic Polynomial Addition Formula Linear Programming Method
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