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A Note on “Pattern Variants on a Square Field”

Published online by Cambridge University Press:  01 January 2025

John W. Moon
John W. Moon*
Affiliation:
University of Alberta
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Abstract

It is shown how results of Prokhovnik on the number of pattern variants that may be formed by k markers on a square network of m2 positions may be derived more simply by means of a combinatorial theorem of Pólya's, which may also be used to solve systematically many other problems of this type.

Type
Original Paper
Information
Psychometrika , Volume 28 , Issue 1 , March 1963 , pp. 93 - 95
Copyright
Copyright © 1963 The Psychometric Society

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References

Harary, F. The number of linear, directed, rooted, and connected graphs. Trans. Amer. math. Soc., 1955, 78, 445–463.CrossRefGoogle Scholar
Pólya, G. Kombinatorische Anzahlbestimmungen für Gruppen, Graphen, und chemische Verbindungen. Acta Math., 1937, 68, 145–254.CrossRefGoogle Scholar
Prokhovnik, S. J. Pattern variants on a square field. Psychometrika, 1959, 24, 329–341.CrossRefGoogle Scholar
Riordan, J. An introduction to combinatorial analysis, New York: Wiley, 1958.Google Scholar