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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Construction of Steiner quadruple systems having large numbers of nonisomorphic associated Steiner triple systems
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by Charles C. Lindner
Proc. Amer. Math. Soc. 49 (1975), 256-260
DOI: https://doi.org/10.1090/S0002-9939-1975-0389617-6

Abstract:

If $(Q,q)$ is a Steiner quadruple system and $x$ is any element in $Q$ it is well known that the set ${Q_x} = Q\backslash \{ x\}$ equipped with the collection $q(x)$ of all triples $\{ a,b,c\}$ such that $\{ a,b,c,x\} \in q$ is a Steiner triple system. A quadruple system $(Q,q)$ is said to have at least $n$ nonisomorphic associated triple systems (NATS) provided that for at least one subset $X$ of $Q$ containing $n$ elements the triple systems $({Q_x},q(x))$ and $({Q_y},q(y))$ are nonisomorphic whenever $x \ne y \in X$. Prior to the results in this paper the maximum number of known NATS for any quadruple system was 2. The main result in this paper is the construction for each positive integer $t$ of a quadruple system having at least $t$ NATS.
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 49 (1975), 256-260
  • MSC: Primary 05B05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0389617-6
  • MathSciNet review: 0389617