Abstract
A Steiner quadruple system is an ordered pair (X,Q) where X is a finite set and Q is a set of 4-subsets of X such that every 3-subset of X is contained in a unique member of Q.
This paper gives a structure for studying all the known recursive constructions for quadruple systems. The structure is then applied to existence problems for quadruple systems with subsystems.
Keywords
- Induction Hypothesis
- Unique Member
- Existence Problem
- Direct Construction
- Recursive Construction
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This work forms part of the author's research towards a Ph.D. at the University of Newcastle.
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References
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© 1981 Springer-Verlag
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Hartman, A. (1981). A singular direct product for quadruple systems. In: McAvaney, K.L. (eds) Combinatorial Mathematics VIII. Lecture Notes in Mathematics, vol 884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091821
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DOI: https://doi.org/10.1007/BFb0091821
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10883-2
Online ISBN: 978-3-540-38792-3
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