Publication date: 27 December 2023
Volume: Vol 58
Issue: Svezak 2
Pages: 233-245
DOI: 10.3336/gm.58.2.06
Izvorni znanstveni članak
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
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.
Classification, Steiner triple system, subsystem
312013
16.8.2024.
Posjeta: 157 *