Enumerating Steiner triple systems
Loading...
Access rights
openAccess
URL
Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
Date
2023-10
Major/Subject
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
Other note
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