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Symmetric functions and spherical t-designs in \(\pmb {\mathbb {R}^2}\)

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Abstract

Given k points in \(S^1\) satisfying certain conditions which are determined through their symmetric functions, we introduce a method for constructing spherical t-designs in \(\mathbb {R}^2\) with \(2t+k\) elements. This approach points toward a better understanding of the space of spherical t-designs as well as provides a systematic way to obtain examples.

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Acknowledgements

The author would like to thank Professor Patricia Morillas (Departamento de Matemática, Universidad Nacional de San Luis-CONICET) for suggesting the present research subject and for many useful discussions that helped him to clarify the ideas and concepts developed in this article. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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  1. Departamento de Matemática, Facultad de Ciencias Fisico Matemáticas, Universidad Nacional de San Luis, Ejército de Los Andes 950, D5700HHW, San Luis, Argentina

    Federico N. Martínez

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  1. Federico N. Martínez
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Correspondence to Federico N. Martínez.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: On Coding Theory and Combinatorics: In Memory of Vera Pless”.

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Martínez, F.N. Symmetric functions and spherical t-designs in \(\pmb {\mathbb {R}^2}\). Des. Codes Cryptogr. 90, 2563–2581 (2022). https://doi.org/10.1007/s10623-021-00922-3

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  • DOI: https://doi.org/10.1007/s10623-021-00922-3

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