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On a conjecture of Conway

Published online by Cambridge University Press:  24 October 2008

E. C. Milner
E. C. Milner
Affiliation:
Department of Mathematics, University of Reading
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Extract

Small letters denote non-negative integers and capital letters denote sets. The set theoretic difference of A and B is A − B. The empty set is ø and |A| denotes the cardinal of A. We say that A is an immediate extension of B if B ⊂ A and |A − B| = 1. If C is a set of sets we put C(n) = {X: X ∈ C, |X| = n}. A set of sets C, has the property P(k, n) if (i) ø ∈ C and (ii) if X ∈ C(i) and i < n, then C(i + 1) contains at least k immediate extensions of X. We assume throughout that k ≥ 1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 1 , January 1966 , pp. 43 - 44
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

(1)Croft, H. T.Research Problems (April, 1965). Peterhouse, Cambridge.Google Scholar