Geodesic
Another Enumeration of Trees
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1077-1086

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Knuth, Donald E. Another Enumeration of Trees. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1077-1086. doi: 10.4153/CJM-1968-104-8
@article{10_4153_CJM_1968_104_8,
     author = {Knuth, Donald E.},
     title = {Another {Enumeration} of {Trees}},
     journal = {Canadian journal of mathematics},
     pages = {1077--1086},
     year = {1968},
     volume = {20},
     number = {1},
     doi = {10.4153/CJM-1968-104-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-104-8/}
}
TY  - JOUR
AU  - Knuth, Donald E.
TI  - Another Enumeration of Trees
JO  - Canadian journal of mathematics
PY  - 1968
SP  - 1077
EP  - 1086
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-104-8/
DO  - 10.4153/CJM-1968-104-8
ID  - 10_4153_CJM_1968_104_8
ER  - 
%0 Journal Article
%A Knuth, Donald E.
%T Another Enumeration of Trees
%J Canadian journal of mathematics
%D 1968
%P 1077-1086
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-104-8/
%R 10.4153/CJM-1968-104-8
%F 10_4153_CJM_1968_104_8

[1] 1. Austin, T. L., The enumeration of point labelled chromatic graphs and trees, Can. J. Math. 12 (1960), 535–545. Google Scholar

[2] 2. Cayley, A., A theorem on trees, Collected mathematical papers, Volume 13, 26–28. Google Scholar

[3] 3. Good, I. J., The generalization of Lagrange's expansion and the enumeration of trees, Proc. Cambridge Philos. Soc. 61 (1965), 499–517. Google Scholar

[4] 4. Gould, H. W., Note on problems 4960 and 4984, Amer. Math. Monthly 69 (1962), 572. Google Scholar

[5] 5. Knuth, D., Oriented subtrees of an arc digraph, J. Combinatorial Theory 3 (1967), 309–314. Google Scholar

[6] 6. Moon, J. W., Various proofs of Cayley's formula for counting trees, A Seminar on Graph Theory, Harary, F., ed. (Holt, Rinehart, and Winston, 1967, pp. 70–78). Google Scholar

[7] 7. Prufer, H., Neuer Beweis eines Satzes iiber Permutationen, Arch. Math, und Phys. 27 1918), 142–144. Google Scholar

[8] 8. Raney, G., A formal solution of Yf*Li Ai exp(BiX) = X, Can. J. Math. 16 (1964), 755–762. Google Scholar

[9] 9. Riordan, J., The enumeration of labeled trees by degrees, Bull. Amer. Math. Soc. 72 (1966), 110–112. Google Scholar

[10] 10. Scoins, H. I., The number of trees with nodes of alternate parity, Proc. Cambridge Philos. Soc. 58 (1962), 12–16. Google Scholar

[11] 11. Tutte, W., The dissection of equilateral triangles into equilateral triangles, Proc. Cambridge Philos. Soc. 15 (1948), 463–482. Google Scholar

Cité par Sources :