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Steiner Triple Systems of Order 21 with Subsystems

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arxiv 2104.06825 v2 pith:BZM2RYLW submitted 2021-04-14 math.CO

Daniel Heinlein , Patric R. J. Österg{aa}rd This is my paper · ORCID
classification math.CO
keywords classesisomorphismordersteinersubsystemssystemstriplecase
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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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  1. On the number of small Steiner triple systems with Veblen points

    math.CO 2024-11 conditional novelty 6.0 of 10

    The authors enumerate the non-isomorphic Steiner triple systems of orders 19, 27 and 31 that contain Veblen points: 3, 1736, and 2 with exactly three Veblen points, plus partial counts for order 31 with one Veblen point.

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