Geodesic
A combinatorial derivation of the number of labeled forests
Journal of integer sequences, Tome 6 (2003) no. 4
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.
Classification : 05C05
Keywords: tree, labeled forest, partially-paired rooted n-forest, inversion-initiating vertex, weight-reversing involution 
@article{JIS_2003__6_4_a7,
     author = {Callan,  David},
     title = {A combinatorial derivation of the number of labeled forests},
     journal = {Journal of integer sequences},
     year = {2003},
     volume = {6},
     number = {4},
     zbl = {1064.05083},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a7/}
}
TY  - JOUR
AU  - Callan,  David
TI  - A combinatorial derivation of the number of labeled forests
JO  - Journal of integer sequences
PY  - 2003
VL  - 6
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a7/
LA  - en
ID  - JIS_2003__6_4_a7
ER  - 
%0 Journal Article
%A Callan,  David
%T A combinatorial derivation of the number of labeled forests
%J Journal of integer sequences
%D 2003
%V 6
%N 4
%U http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a7/
%G en
%F JIS_2003__6_4_a7
Callan,  David. A combinatorial derivation of the number of labeled forests. Journal of integer sequences, Tome 6 (2003) no. 4. http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a7/