Open Access
February, 2021 Classification of Spherical $2$-distance $\{4,2,1\}$-designs by Solving Diophantine Equations
Eiichi Bannai, Etsuko Bannai, Ziqing Xiang, Wei-Hsuan Yu, Yan Zhu
Taiwanese J. Math. 25(1): 1-22 (February, 2021). DOI: 10.11650/tjm/200601


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.


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Eiichi Bannai. Etsuko Bannai. Ziqing Xiang. Wei-Hsuan Yu. Yan Zhu. "Classification of Spherical $2$-distance $\{4,2,1\}$-designs by Solving Diophantine Equations." Taiwanese J. Math. 25 (1) 1 - 22, February, 2021.


Received: 21 January 2020; Revised: 29 May 2020; Accepted: 11 June 2020; Published: February, 2021
First available in Project Euclid: 25 June 2020

Digital Object Identifier: 10.11650/tjm/200601

Primary: 05B30 , 05E30 , 11D41

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

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

Vol.25 • No. 1 • February, 2021
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