Original scientific paper

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

Steiner triple systems of order 21 with subsystems

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

24.4.2025.

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