On the Altitude of Nodes in Random Trees
Canadian journal of mathematics, Tome 30 (1978) no. 5, pp. 997-1015

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

Let Tn denote a tree with n nodes that is rooted at node r. (For definitions not given here see [4] or [10].) The altitude of a node u in Tn is the distance α = α (u, Tn) between r and u in Tn. The width of Tn at altitude is the number Wk = Wk(Tn) of nodes at altitude in Tn, where = 0, 1, ...
Meir, A.; Moon, J. W. On the Altitude of Nodes in Random Trees. Canadian journal of mathematics, Tome 30 (1978) no. 5, pp. 997-1015. doi: 10.4153/CJM-1978-085-0
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[1] 1. Bender, E. A., Asymptotic methods in enumeration, SIAM Review 16 (1974), 485–515. Google Scholar

[2] 2. Cayley, A., On the analytical forms called trees, Philosophical Magazine 28 (1858), 374-378. Collected Mathematical Papers, Cambridge, 4 (1891), 112–115.) Google Scholar

[3] 3. Darboux, G., Mémoire sur l'approximation des fonctions de très grands nombres, et sur une classe étendu de développements en série, Journal de Math. Pures et Appliquées (3) 4 (1878), 5–56. Google Scholar

[4] 4. Harary, F. and Palmer, E., Graphical enumeration (Academic Press, New York, 1973). Google Scholar

[5] 5. Harary, F., Robinson, R. W., and Schwenk, A. J., Twenty-step algorithm for determining the asymptotic number of trees of various species, J. Austral. Math. Soc. 20 (1975), 483–503. Google Scholar

[6] 6. Knuth, D. E., The art of computer programming, III (Addison-Wesley, Reading, 1973). Google Scholar

[7] 7. Meir, A. and Moon, J. W., The distance between points in random trees, J. Comb. Theory 8 (1970), 99–103. Google Scholar

[8] 8. Meir, A. and Moon, J. W., The expected node-independence number of various types of trees, Recent Advances in Graph Theory (Academia, Prague, 1975), 351–363. Google Scholar

[9] 9. Meir, A. and Moon, J. W., Packing and covering constants for certain families of trees, I, J. Graph Theory 1 (1977), 157–174. Google Scholar

[10] 10. Moon, J. W., Counting labelled trees (Canadian Mathematical Congress, Montreal, 1970). Google Scholar

[11] 11. Moon, J. W., The distance between nodes in recursive trees, Proceedings of the British Combinatorial Conference, 1973 (Cambridge, 1974), 125–132. Google Scholar

[12] 12. Otter, R., The number of trees, Ann. of Math. 49 (1948), 583–599. Google Scholar

[13] 13. Palmer, E. M. and Schwenk, A. J., On the number of trees in a random forest (abstract), A.M.S. Notices 23 (1976), A-2. Google Scholar

[14] 14. Pôlya, G., Kombinatorische Anzahlbestimmungen fur Gruppen, Graphen und chemische Verbindungen, Acta Mathematica 68 (1937), 145–254. Google Scholar

[15] 15. Stepanov, V. E., On the distribution of the number of vertices in strata of a random tree, Th. Prob. and its Appl. 14 (1969), 65–78. Google Scholar

[16] 16. Volosin, Ju. M., Enumeration of the terms of object domains according to the depth of embedding, Sov. Math. Dokl. 15 (1974), 1777–1782. Google Scholar

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