Abstract
We study the number of records inacomplete binary tree with randomly labeled vertices or edges. Equivalently,we may study the number of random cuttings requiredto eliminate a completebinary tree.
The distribution is after normalization asymptotically a periodic function of lg n — lg lg n; thusthere is no true asymptotic distribution but a family of limits of different subsequences; these limits aresimilar to a 1-stabledistribution but have some periodic fluctuations.
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References
P. Chassaing & R. Marchand. In preparation.
W. Feller, AnIntroduction to Probability Theory and Its Applications. Vol. II.Second edition, Wiley, New York 1971.
S. Janson, Random cutting and records in deterministic and random trees. Preprint, 2003. Available from http://www.math.uu.se/~svante/papers
O. KallenbergFoundations of Modern Probability.2nd ed., Springer-Verlag, New York, 2002.
D.E. KnuthThe Art of Computer Programming. Vol. 1: Fundamental Algorithms.3nd ed., Addison-Wesley, Reading, Mass., 1997.
A. Meir & J.W. Moon, Cutting down random trees.J. Australian Math. Soc. 11(1970), 313–324.
A. Panholzer, Cutting down very simple trees. Preprint, 2003.
A. Panholzer, Non-crossing trees revisited: cutting down and spanning subtrees.Proceedings Discrete Random Walks 2003Cyril Banderier and Christian Krattenthaler, Eds.,Discr. Math. Theor. Comput. Sci. AC (2003), 265–276.
A. Rényi, (1962). On the extreme elements of observations. MTA III, Oszt. Közl. 12 (1962) 105–121. Reprinted in Collected Works, Vol III, pp. 50–66, Akadémiai Kiadó, Budapest, 1976.
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Janson, S. (2004). Random Records and Cuttings in Complete Binary Trees. In: Drmota, M., Flajolet, P., Gardy, D., Gittenberger, B. (eds) Mathematics and Computer Science III. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7915-6_24
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DOI: https://doi.org/10.1007/978-3-0348-7915-6_24
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9620-7
Online ISBN: 978-3-0348-7915-6
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