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Paper detail

Steiner Triple Systems of Order 21 with Subsystems

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.

preprint2022arXivOpen access
Daniel HeinleinPatric R. J. Östergård
math.CO
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Daniel HeinleinPatric R. J. Östergård

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