A class of Steiner triple systems of order 21 and associated Kirkman systems
Open Access
- 1 January 1981
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 37 (155) , 209-222
- https://doi.org/10.1090/s0025-5718-1981-0616374-9
Abstract
We examine a class of Steiner triple systems or order 21 with an automorphism consisting of three disjoint cycles of length 7. We exhibit explicitly all members of this class: they number 95 including the 7 cyclic systems. We then examine resolvability of the obtained systems; only 6 of the 95 are resolvable yielding a total of 30 nonisomorphic Kirkman triple systems of order 21. We also list several invariants of the systems and investigate their further properties.Keywords
This publication has 10 references indexed in Scilit:
- Combinatorial TheoryPublished by Wiley ,1988
- Steiner triple systems with rotational automorphismsDiscrete Mathematics, 1981
- On the existence of doubly resolvable Kirkman systems and equidistant permutation arraysDiscrete Mathematics, 1980
- Room Squares GeneralizedPublished by Elsevier ,1980
- Non-Isomorphic Reverse Steiner Triple Systems of Order 19Published by Elsevier ,1980
- On Cyclic Steiner 2-DesignsPublished by Elsevier ,1980
- Almost All Steiner Triple Systems Are AsymmetricPublished by Elsevier ,1980
- GENERALIZED HOWELL DESIGNSAnnals of the New York Academy of Sciences, 1979
- Nonisomorphic Steiner triple systemsMathematische Zeitschrift, 1974
- Kirkman paradesBulletin of the American Mathematical Society, 1922