Enumerating Steiner triple systems

Daniel Heinlein; Patric R.J. Östergård

doi:10.1002/jcd.21906

Enumerating Steiner triple systems

Daniel Heinlein^*, Patric R.J. Östergård

^*Corresponding author for this work

Department of Information and Communications Engineering

Research output: Contribution to journal › Article › Scientific › peer-review

2 Citations (Scopus)

78 Downloads (Pure)

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
Pages (from-to)	479-495
Number of pages	17
Journal	Journal of Combinatorial Designs
Volume	31
Issue number	10
Early online date	2023
DOIs	https://doi.org/10.1002/jcd.21906
Publication status	Published - Oct 2023
MoE publication type	A1 Journal article-refereed

Keywords

classification
counting
regular graph
Steiner triple system

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10.1002/jcd.21906Licence: CC BY

J of Combinatorial Designs - 2023 - HeinleinFinal published version, 632 KBLicence: CC BY

Cite this

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title = "Enumerating Steiner triple systems",

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.",

keywords = "classification, counting, regular graph, Steiner triple system",

author = "Daniel Heinlein and {\"O}sterg{\aa}rd, {Patric R.J.}",

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

year = "2023",

month = oct,

doi = "10.1002/jcd.21906",

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T1 - Enumerating Steiner triple systems

AU - Heinlein, Daniel

AU - Östergård, Patric R.J.

N1 - 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.

PY - 2023/10

Y1 - 2023/10

N2 - 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.

AB - 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.

KW - classification

KW - counting

KW - regular graph

KW - Steiner triple system

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U2 - 10.1002/jcd.21906

DO - 10.1002/jcd.21906

M3 - Article

AN - SCOPUS:85165175156

SN - 1063-8539

VL - 31

SP - 479

EP - 495

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

IS - 10

ER -

Enumerating Steiner triple systems

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SubspaceCodes: Constructions and Classifications of Subspace Codes and Related Structures for Communication Networks

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Enumerating Steiner triple systems

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Keywords

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SubspaceCodes: Constructions and Classifications of Subspace Codes and Related Structures for Communication Networks

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