Abstract
We derive asymptotic results on the distribution of the number of descendants in simply generated trees. Our method is based on a generating function approach and complex contour integration.
1This research has been supported by the Austrian Science Foundation FWF, grant P10187- MAT, and by the Stiftung Aktion Österreich—Ungarn, grant 34oeu24.
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References
D. J. Aldous, The continuum random tree II: an overview, Stochastic Analysis, M. T. Barlow and N. H. Bingham, Eds., Cambridge University Press 1991, 23–70.
G. Baron, M. Drmota and L. Mutafchief, Predecessors in random mappings, Combin. Probab. Comput. 5, No. 4, (1996), 317–335.
M. Drmota, The height distribution of leaves in rooted trees, Discr. Math. Appl 4 (1994), 45–58 (translated from Diskretn. Mat. 6 (1994), 67–82).
M. Drmota and B. Gittenberger, On the profile of random trees, Random Struct. Alg. 10 (1997), 421–451.
M. Drmota and M. Soria, Marking in combinatorial constructions: generating functions and limiting distributions, Theor. Comput. Sci. 144 (1995), 67–99.
M. Drmota and M. Soria, Images and preimages in random mappings, SIAM J. Discrete Math. 10, No.2 (1997), 246–269.
P. Flajolet and A. M. Odlyzko, Singularity analysis of generating functions, SIAM J. Discrete Math. 3, 2 (1990), 216–240.
P. Flajolet and J. S. Vitter, Average-Case Analysis of Algorithms and Data Structures, in Handbook of Theoretical Computer Science, J. van Leeuwen, Ed., vol. A: Algorithms and Complexity. North Holland, 1990, ch. 9, pp. 431–524.
B. Gittenberger, On the number of predecessors in constrained random mappings, Stat. Probab. Letters 36 (1997), 29–34.
B. Gittenberger, On the contour of random trees, SIAM J. Discrete Math. 12, No.4 (1999), 434–458.
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, New York, 1983.
W. Gutjahr and G. CH. Pflug, The asymptotic contour process of a binary tree is a Brownian excursion, Stochastic Process. Appl. 41 (1992), 6989.
A. Meir and J. W. Moon, On the Altitude of Nodes in Random Trees, Can. J. Math. 30 (1978), 997–1015.
C. MartĂnez, A. Panholzer and H. Prodinger, On the number of descendants and ascendants in random search trees, Electronic Journal of Combinatorics 5 (1998), Research paper R20, 26 p.; printed version J. Comb. 5 (1998), 267–302.
A. Panholzer and H. Prodinger, Descendants and ascendants in binary trees, Discrete Mathematics and Theoretical Computer Science 1 (1997), 247–266.
Whittaker, E. T. and Watson, G. N., A Course of Modern Analysis, reprint of the 4th edn., Cambridge University Press, 1996.
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Gittenberger, B. (2000). The Number of Descendants in Simply Generated Random Trees. In: Gardy, D., Mokkadem, A. (eds) Mathematics and Computer Science. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8405-1_6
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DOI: https://doi.org/10.1007/978-3-0348-8405-1_6
Publisher Name: Birkhäuser, Basel
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