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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Steiner triple systems of order $19$ with nontrivial automorphism group
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by Charles J. Colbourn, Spyros S. Magliveras and D. R. Stinson PDF
Math. Comp. 59 (1992), 283-295 Request permission

Abstract:

There are 172,248 Steiner triple systems of order 19 having a nontrivial automorphism group. Computational methods suitable for generating these designs are developed. The use of tactical configurations in conjunction with orderly algorithms underlies practical techniques for the generation of the designs, and the subexponential time isomorphism technique for triple systems is improved in practice to test isomorphisms of the designs. The automorphism group of each of the triple systems is computed, and a summary presented of the number of systems with each possible type of automorphism.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 59 (1992), 283-295
  • MSC: Primary 05B07; Secondary 20B25
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1134722-8
  • MathSciNet review: 1134722