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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.
Original language | English |
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Pages (from-to) | 479-495 |
Number of pages | 17 |
Journal | Journal of Combinatorial Designs |
Volume | 31 |
Issue number | 10 |
Early online date | 2023 |
DOIs | |
Publication status | Published - Oct 2023 |
MoE publication type | A1 Journal article-refereed |
Keywords
- classification
- counting
- regular graph
- Steiner triple system
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Dive into the research topics of 'Enumerating Steiner triple systems'. Together they form a unique fingerprint.Projects
- 1 Finished
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SubspaceCodes: Constructions and Classifications of Subspace Codes and Related Structures for Communication Networks
Heinlein, D. (Principal investigator)
01/09/2020 → 31/08/2023
Project: Academy of Finland: Other research funding