Classification of spherical 2-distance {4, 2, 1}-designs by solving diophantine equations

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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalTaiwanese Journal of Mathematics
Volume25
Issue number1
DOIs
StatePublished - Feb 2021

Keywords

  • 2-distance set
  • Diophantine equation
  • Spherical design
  • Strongly regular graph

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