Enumerating Steiner triple systems
Copyright policy )Enumerating Steiner triple systems
AbstractSteiner 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.
- Aalto University Finland
Steiner triple system, Triple systems, ta111, Exact enumeration problems, generating functions, 05B07, classification, regular graph, FOS: Mathematics, counting, Mathematics - Combinatorics, Combinatorics (math.CO)
Steiner triple system, Triple systems, ta111, Exact enumeration problems, generating functions, 05B07, classification, regular graph, FOS: Mathematics, counting, Mathematics - Combinatorics, Combinatorics (math.CO)
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