Journal of Integer Sequences, Vol. 6 (2003), Article 03.4.7

A Combinatorial Derivation of the Number of Labeled Forests


David Callan
Department of Statistics
University of Wisconsin-Madison
1210 W. Dayton St
Madison, WI \ 53706-1693
USA

Abstract: Lajos Takács gave a somewhat formidable alternating sum expression for the number of forests of unrooted trees on n labeled vertices. Here we use a weight-reversing involution on suitable tree configurations to give a combinatorial derivation of Takács' result.

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(Concerned with sequence A001858 .)

Received October 3, 2003; revised version received November 3, 2003. Published in Journal of Integer Sequences January 15, 2004.

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