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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A class of Steiner triple systems of order $21$ and associated Kirkman systems
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by Rudolf A. Mathon, Kevin T. Phelps and Alexander Rosa PDF
Math. Comp. 37 (1981), 209-222 Request permission

Addendum: Math. Comp. 64 (1995), 1355-1356.

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.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 209-222
  • MSC: Primary 05B07; Secondary 51E10
  • DOI: https://doi.org/10.1090/S0025-5718-1981-0616374-9
  • MathSciNet review: 616374