Abstract
This paper deals with the average number of nodes with a special property in binary trees with n nodes. Generating functions are set up and considered as analytic functions. A detailed singularity analysis allows to get asymptotic formulas for the considered numbers. The local expansions are derived by use of the Mellin transform. The asymptotic expansion involves periodic terms; the Fourier coefficients are computed in terms of Riemann’s ξ-functions etc.
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Literatur
E.A. BENDER, Asymptotic methods in enumeration, SIAM Reviews 16 (1974), 485–515.
N.G. de BRUIJN, D.E. KNUTH, S.O. RICE, The average height of planted plane trees, in: Graph Theory and Computing (R.C. Read, Ed.), 15–22, Academic Press, New York-London, 1972.
P. FLAJOLET, Analyse d’algorithmes de manibulation d’arbres et de fichiers, Cahiers du BURO, 34–35 (1981), 1–209.
P. FLAJOLET, A. ODLYZKO, The average height of binary trees and other simple trees, J. Comput. Syst. Sci. 25 (1982), 142–158.
P. FLAJOLET, J.-C. RAOULT, J. VUILLEMIN, The number of registers required for evaluating arithmetical expressions, Theoretical Computer Science 9 (1979), 99–125.
P.FLAJOLET, H.PRODINGER, Register allocation for unary-binary trees, SIAM J. on Computing, im Druck.
R. JUNGEN, Sur les séries de Taylor n’ayant que des singularités algébrologarithmiques sur leur cercle de convergence, Commentarii Math. Helvetici 3 (1931), 266–306.
R. KEMP, The average number of registers to evaluate a binary tree optimally, Acta Informatica 11 (1979), 363–372.
D.E.KNUTH, The art of computer programming, Vol. 1, Addison Wesley 1968.
A. MEIR, J.W. MOON, J.R. POUNDER, On the order of random channel networks, SIAM J. Alg. Discr. Meth. 1 (1980), 25–33.
J.W. MOON, On Horton’s Law for random channel networks, Annals of Discrete Mathematics 8 (1980), 117–121.
A. ODLYZKO, Periodic oscillations of coefficients of power series that satisfy functional equations, Advances in Mathematics 44 (1982), 180–205.
H. PRODINGER, The influence of the nodes on the leftsided height of a binary tree, submitted.
H. PRODINGER, R.F. TICHY, Über ein zahlentheoretisches Problem aus der Informatik, Sitzungsberichte der Österreichischen Akademie der Wissenschaften, im Druck.
E.T. WHITTAKER, G.N. WATSON, A course of modern analysis, Cambridge University Press, 1927.
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© 1985 Springer-Verlag
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Prodinger, H. (1985). Die Bestimmung Gewisser Parameter Bei Binären Bäumen Mit Hilfe Analytischer Methoden. In: Hlawka, E. (eds) Zahlentheoretische Analysis. Lecture Notes in Mathematics, vol 1114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101650
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DOI: https://doi.org/10.1007/BFb0101650
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Online ISBN: 978-3-540-39281-1
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