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Another Enumeration of Trees

Published online by Cambridge University Press:  20 November 2018

Donald E. Knuth
Donald E. Knuth*
Affiliation:
California Institute of Technology, Pasadena, California
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Given a set of vertices which have each been assigned one of the colours C1, C2, …, Cm, with nj vertices Cj, a formula is derived for the number of oriented trees on these vertices, having a designated root, and subject to any number of restrictions of the form “no arc goes from a vertex of colour Ci to a vertex of colour Cj”. The formula is based on a combinatorial construction which defines a correspondence between such trees and certain sequences.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1077 - 1086
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

This research was partially supported by NSF Grant GP 3909.

References

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