Abstract
For n independently distributed geometric random variables we consider the average length of the m-th run, for fixed m and n → ∞. One particular result is that this parameter approaches 1 + q.
In the limiting case q → 1 we thus rederive known results about runs in permutations.
This research was partially conducted while the author was a guest of the projet Algo at INRIA, Rocquencourt. The funding came from the Austrian-French “Amadée” cooperation.
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References
Aigner, M.: Combinatorial Theory. Springer, Heidelberg (1997); Reprint of the 1979 edn.
Andrews, G.E.: The Theory of Partitions. Encyclopedia of Mathematics and its Applications, vol. 2. Addison-Wesley, Reading (1976)
Comtet, L.: Advanced Combinatorics. Reidel, Dordrecht (1974)
Flajolet, P., Gardy, D., Thimonier, L.: Birthday paradox, coupon collectors, caching algorithms, and self-organizing search. Discrete Applied Mathematics 39, 207–229 (1992)
Flajolet, P., Odlyzko, A.: Singularity analysis of generating functions. SIAM Journal on Discrete Mathematics 3, 216–240 (1990)
Knuth, D.E.: The Art of Computer Programming, 2nd edn. Sorting and Searching, vol. 3. Addison-Wesley, Reading (1973)
Prodinger, H.: Combinatorial problems of geometrically distributed random variables and applications in computer science. In: Strehl, V., König, R. (eds.) Publications de l’IRMA (Stra\({\ss}\)bourg), vol. 30, pp. 87–95 (1993)
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Prodinger, H. (2000). Combinatorics of Geometrically Distributed Random Variables: Length of Ascending Runs. In: Gonnet, G.H., Viola, A. (eds) LATIN 2000: Theoretical Informatics. LATIN 2000. Lecture Notes in Computer Science, vol 1776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719839_47
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DOI: https://doi.org/10.1007/10719839_47
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