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The number of plane trees with a given partition

Published online by Cambridge University Press:  26 February 2010

F. Harary  and
W. T. Tutte
F. Harary
Affiliation:
University of Michigan.
W. T. Tutte
Affiliation:
University of Waterloo.
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Extract

This note is a continuation of the articles [6] and [2]. In [1], trees with a given partition α = (a1; a2, …), where ai is the number of vertices (points) of valency (degree) i were enumerated. After the determination of the number of plane trees in [2], the number of planted plane trees with a given partition α was found explicitly in [6]. In the present note, the number of plane trees with a given partition is expressed as a function of the number of planted trees with a given partition. The method, which is not new, consists of an application of the enumeration techniques of Otter [3] and Pólya [4]; it was used in [1] and also by Riordan [5].

Type
Research Article
Information
Mathematika , Volume 11 , Issue 2 , December 1964 , pp. 99 - 101
Copyright
Copyright © University College London 1964

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References

1. Harary, F. and Prins, G., “The number of homeomorphically irreducible trees, and other species”, Acta Math., 101 (1959), 141–162.CrossRefGoogle Scholar
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