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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Abstract

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

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

Dates
First available in Project Euclid: 25 June 2020

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1593050477

Digital Object Identifier
doi:10.11650/tjm/200601

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

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

Citation

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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References

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