Geodesic
Labeled trees, functions, and an algebraic identity
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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We give a short and direct proof of a remarkable identity that arises in the enumeration of labeled trees with respect to their indegree sequence, where all edges are oriented from the vertex with lower label towards the vertex with higher label. This solves a problem posed by Shin and Zeng in a recent article. We also provide a generalization of this identity that translates to a formula for the number of rooted spanning forests with given indegree sequence.
DOI : 10.37236/675
Classification : 05C30, 05A19, 05C05
Mots-clés : rooted spanning forests 
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     author = {Stephan Wagner},
     title = {Labeled trees, functions, and an algebraic identity},
     journal = {The electronic journal of combinatorics},
     year = {2011},
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     number = {1},
     doi = {10.37236/675},
     zbl = {1337.05056},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/675/}
}
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Stephan Wagner. Labeled trees, functions, and an algebraic identity. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/675

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