Author:
Heinlein Daniel, ,Ostergård Patric R J,
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.
Publisher
University of Zagreb, Faculty of Science, Department of Mathematics
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