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Abstract: Introduction A wide variety of new results in combinatorial enumeration have been obtained recently. Many of these results were prompted by new problems in computer science, while others answered old questions in combinatorics and other fields. The purpose of this note is to survey a subset of these new results, namely those dealing with tree enumeration. A selection of tree enumeration results is presented, together with a discussion of the methods that led to their derivation. No complete... (Update)
Context of citations to this paper: More
.... is very simple, especially when compared to some of the other asymptotic enumeration methods that are used in other situations (cf. [4,20]) The main difficulty is to obtain the generating functions for the quantities that are of interest and show that they satisfy the...
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3: Central and local limit theorems applied to asymptotic enumeration (context) - Bender - 1973
3: The Art of Computer Programming Vol (context) - Knuth - 1968
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BibTeX entry: (Update)
A. M. Odlyzko, Some new methods and results in tree enumeration, Congressus Numerantium 42 (1984), 27-52. http://citeseer.ist.psu.edu/odlyzko84some.html More
@misc{ odlyzko84some,
author = "A. Odlyzko",
title = "Some new methods and results in tree enumeration",
text = "A. M. Odlyzko, Some new methods and results in tree enumeration, Congressus
Numerantium 42 (1984), 27-52.",
year = "1984",
url = "citeseer.ist.psu.edu/odlyzko84some.html" }
Citations (may not include all citations):1450 The Design and Analysis of Computer Algorithms (context) - Aho, Hopcroft et al. - 1974
157 The Art of Computer Programming: Sorting and Searching (context) - Knuth - 1973
116 Graphical Enumeration (context) - Harary, Palmer - 1973
66 the altitude of nodes in random trees (context) - Meir, Moon - 1978
66 The Art of Computer Programming: Fundamental Algorithms (context) - Knuth - 1968
66 Iterated Maps on the Interval as Dynamical Systems (context) - Collet, Eckmann - 1980
59 Lectures on Functional Equations and Their Applications (context) - Aczel - 1966
48 Asymptotic methods in enumeration (context) - Bender - 1974
35 The average height of binary trees and other simple trees (context) - Flajolet, Odlyzko - 1982
33 Asymptotic Methods in Analysis (context) - de Bruijn - 1958
28 Invariant sets under iteration of rational functions (context) - Brolin - 1965
18 The number of trees (context) - Otter - 1948
13 A generalization of Stirling's formula (context) - Hayman - 1956
13 Asymptotic expansions for the coefficients of analytic funct.. (context) - Harris, Schoenfeld - 1968
12 Functional Equations in a Single Variable (context) - Kuczma - 1968
11 the height of trees (context) - Renyi, Szekeres - 1967
10 Asymptotic expansions for the coefficients of analytic gener.. - Odlyzko, Richmond
9 Canadian Mathematical Congress (context) - Moon, Trees - 1970
9 Periodic oscillations of coefficients of power series that s.. (context) - Odlyzko - 1982
8 Constant time generation of free trees (context) - Wright, Richmond et al.
6 Twenty-step algorithm for determining the asymptotic number .. (context) - Harary, Robinson et al. - 1975
6 Memoire sur l'iteration des fonctions rationnelles (context) - Julia - 1918
6 On random binary trees (context) - Brown, Shubert
5 Some doubly exponential sequences (context) - Aho, Sloane - 1973
5 Distribution of labelled trees by diameter (context) - Szekeres - 1982
5 manuscript in preparation (context) - Odlyzko, Richmond
4 Regular iteration of real and complex functions (context) - Szekeres - 1958
4 the distribution of the number of vertices in strata of a ra.. (context) - Stepanov - 1969
4 Memoire sur l'approximation des fonctions de tres grands nom.. (context) - Darboux
3 Limit distributions for coefficients of iterates of polynomi.. - Flajolet, Odlyzko
2 Exploring binary trees and other simple trees (context) - Flajolet, Odlyzko - 1980
2 Fibonacci Quart (context) - Reingold, on et al. - 1979
2 Concerning periodicity in the asymptotic behavior of partiti.. (context) - Erdo, Richmond - 1976
2 Enumeration of AVL-trees (context) - Odlyzko
2 On Mahler's partition problem (context) - de Bruijn - 1948
1 Kombinatorische Anzahlbestimmungen fu (context) - Polya - 1937
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