Enumerating Steiner triple systems

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openAccess

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Volume Title

A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

2023-10

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Mcode

Degree programme

Language

en

Pages

17

Series

Journal of Combinatorial Designs

Abstract

Steiner triple systems (STSs) have been classified up to order 19. Earlier estimations of the number of isomorphism classes of STSs of order 21, the smallest open case, are discouraging as for classification, so it is natural to focus on the easier problem of merely counting the isomorphism classes. Computational approaches for counting STSs are here considered and lead to an algorithm that is used to obtain the number of isomorphism classes for order 21: 14,796,207,517,873,771.

Description

Funding Information: The authors thank the referees for their valuable comments. Supported by the Academy of Finland, Grant 331044. Publisher Copyright: © 2023 The Authors. Journal of Combinatorial Designs published by Wiley Periodicals LLC.

Keywords

classification, counting, regular graph, Steiner triple system

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Citation

Heinlein, D & Östergård, P R J 2023, ' Enumerating Steiner triple systems ', Journal of Combinatorial Designs, vol. 31, no. 10, pp. 479-495 . https://doi.org/10.1002/jcd.21906