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Enumerating Steiner Triple Systems

2023/03/02 by Daniel Heinlein, Heinlein, Daniel, Patric R. J. Östergård +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #05B07 #Algorithms and Data Compression #Combinatorics (math.CO) #DNA and Biological Computing #FOS: Mathematics #Genome Rearrangement Algorithms

paper · pdf · doi:10.48550/arxiv.2303.01207

openalex publication_date 2023/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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