Taiwanese Journal of Mathematics

Classification of Spherical $2$-distance $\{4,2,1\}$-designs by Solving Diophantine Equations

Eiichi Bannai, Etsuko Bannai, Ziqing Xiang, Wei-Hsuan Yu, and Yan Zhu

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In algebraic combinatorics, the first step of the classification of interesting objects is usually to find all their feasible parameters. The feasible parameters are often integral solutions of some complicated Diophantine equations, which cannot be solved by known methods. In this paper, we develop a method to solve such Diophantine equations in $3$ variables. We demonstrate it by giving a classification of finite subsets that are spherical $2$-distance sets and spherical $\{4,2,1\}$-designs at the same time.

Article information

Taiwanese J. Math., Advance publication (2020), 22 pages.

First available in Project Euclid: 25 June 2020

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Primary: 05B30: Other designs, configurations [See also 51E30] 05E30: Association schemes, strongly regular graphs 11D41: Higher degree equations; Fermat's equation

$2$-distance set Diophantine equation spherical design strongly regular graph


Bannai, Eiichi; Bannai, Etsuko; Xiang, Ziqing; Yu, Wei-Hsuan; Zhu, Yan. Classification of Spherical $2$-distance $\{4,2,1\}$-designs by Solving Diophantine Equations. Taiwanese J. Math., advance publication, 25 June 2020. doi:10.11650/tjm/200601. https://projecteuclid.org/euclid.twjm/1593050477

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