Abstract
Let \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{A}\)be a finite set of relations of degree n. A number N is found such that if \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{A}\)has cardinality less than N then for every relation R of degree n the following holds: if no member of \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{A}\)is embeddable in R then R has a strict extension in which no member of \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{A}\)is embeddable. In fact, if all members of \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{A}\)are defined on sets with at least n elements this number N is 3s(n,2). \(\mathop {II}\limits_{k = 3}^n\) 2s(n,k).k-1 where s(n,k) are the Stirling numbers of the second kind.
Keywords
- Equivalence Class
- Equivalence Relation
- Binary Relation
- Distinct Element
- Identical Base
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.
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References
C. Berge, Principles of Combinatorics. (Academic Press, 1971)
R. Fraïssé, Course of Mathematical Logic, Vol. 1. (D. Reidel Publishing Company, 1973)
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© 1976 Springer-Verlag
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Gillam, D.W.H. (1976). Bounds of finite relations. In: Casse, L.R.A., Wallis, W.D. (eds) Combinatorial Mathematics IV. Lecture Notes in Mathematics, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097368
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DOI: https://doi.org/10.1007/BFb0097368
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Online ISBN: 978-3-540-37537-1
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