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A combinatorial derivation of the number of labeled forests

David Callan
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Abstract

Lajos Takacs gave a somewhat formidable alternating sum formula 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 Takacs' formula.

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David Callan. 2003-11-16. A combinatorial derivation of the number of labeled forests. https://arxiv.org/abs/math/0311259

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