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arXiv · 2104.06825

Steiner Triple Systems of Order 21 with Subsystems

Daniel Heinlein·Patric R. J. Östergård
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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.

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Daniel Heinlein, Patric R. J. Östergård. 2022-08-24. Steiner Triple Systems of Order 21 with Subsystems. https://arxiv.org/abs/2104.06825

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