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A Theorem for Enumerating Certain Types of Collections
Published online by Cambridge University Press: 20 November 2018
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In this paper, we are concerned with proving a formula for the computation of what is variously called the pattern inventory (e.g., see De Bruijn [2]) or the configuration counting series (e.g., see Harary [3]). Rather than redeveloping a large number of definitions, we shall assume the reader is already familiar with the terminology used by De Bruijn [2].
Polya, in a celebrated paper [4], proved a formula for computing the pattern inventory for all functions f defined on a set D (where D is acted on by a permutation group G), and mapping into a set R (which is called the store) for which the “store enumerator” in known.
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- Copyright © Canadian Mathematical Society 1973
References
1.
Bruijn, N. G. De, Generalization of Poly a's fundamental theorem in enumeration combinatorial analysis, Indag. Math.
21 (1959), 59–69.Google Scholar
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Bruijn, N. G. De, Polyd's theory of counting, Applied combinatorial mathematics, Beckenbach, E. J., ed. (John Wiley and Sons, New York, 1964).Google Scholar
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Polya, G., KombinatorischeAnzahlbestimmungen fur Gruppen, Graphen und Chemische Verbindungen, Acta Math.
68 (1937), 145–254.Google Scholar
5.
Riordan, J., An introduction to combinatorial analysis (John Wiley and Sons, New York, 1958).Google Scholar
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