Kirkman Triple Systems of Orders 21 and 27
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author = {Myra B. Cohen and Charles J. Colbourn and Lee A. Ives and Alan C. H. Ling},
title = {Kirkman Triple Systems of Orders 21 and 27},
year = {}
}
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Abstract:
There are 50,024 Kirkman triple systems of order 21 admitting an automorphism of order 2. There are 13,280 Kirkman triple systems of order 21 admitting an automorphism of order 3. Together with the 192 known systems and some simple exchange operations, this leads to a collection of 63,745 nonisomorphic Kirkman triple systems of order 21. This includes all KTS(21)s having a nontrivial automorphism group. None of these is doubly resolvable. Four are quadrilateral-free, providing the rst examples of such a KTS(21). Exactly one hundred of the systems admit an automorphism of order six having three xed points and three 6-cycles. Generalizing this structure to order 27, we nd 81,558 Kirkman triple systems of order 27 having an automorphism of order eight. AMS Subject Classication: 05B07. Keywords and Phrases: Kirkman triple system, doubly resolvable design, Steiner triple system, constructive enumeration. 1 Introduction A Steiner triple system of order v, denoted STS(v), is ...
