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Glasnik matematički, Vol. 58 No. 2, 2023.

Original scientific paper

https://doi.org/10.3336/gm.58.2.06

Steiner triple systems of order 21 with subsystems

Daniel Heinlein orcid id orcid.org/0000-0002-3429-3572 ; Department of Information and Communications Engineering, Aalto University, 00076 Aalto, Finland
Patric R J Ostergård orcid id orcid.org/0000-0003-0426-9771 ; Department of Information and Communications Engineering, Aalto University, 00076 Aalto, Finland

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Abstract

The smallest open case for classifying Steiner triple systems is
order 21. A Steiner triple system of order 21, an STS\((21)\), can have
subsystems of orders 7 and 9, and it is known that there are
12,661,527,336 isomorphism classes of STS\((21)\)s with sub-STS\((9)\)s.
Here, the classification of STS\((21)\)s with subsystems is completed by
settling the case of STS\((21)\)s with sub-STS\((7)\)s.
There are
116,635,963,205,551 isomorphism classes of such systems. An estimation
of the number of isomorphism classes of STS\((21)\)s is given.

Keywords

Classification, Steiner triple system, subsystem

Hrčak ID:

312013

URI

https://hrcak.srce.hr/312013

Publication date:

22.12.2024.

Visits: 441 *

Publication date: 27 December 2023

Volume: Vol 58

Issue: Svezak 2

Pages: 233-245

DOI: 10.3336/gm.58.2.06

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Classification, Steiner triple system, subsystem

Steiner triple systems of order 21 with subsystems

Daniel Heinlein[1]

Email: -

Patric R J Ostergård[2]

Email: patric.ostergard@aalto.fi

 

[1] Department of Information and Communications Engineering, Aalto University, 00076 Aalto, Finland

[2] Department of Information and Communications Engineering, Aalto University, 00076 Aalto, Finland

Abstract

The smallest open case for classifying Steiner triple systems is order 21. A Steiner triple system of order 21, an STS\((21)\), can have subsystems of orders 7 and 9, and it is known that there are 12,661,527,336 isomorphism classes of STS\((21)\)s with sub-STS\((9)\)s. Here, the classification of STS\((21)\)s with subsystems is completed by settling the case of STS\((21)\)s with sub-STS\((7)\)s. There are 116,635,963,205,551 isomorphism classes of such systems. An estimation of the number of isomorphism classes of STS\((21)\)s is given.

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