Abstract
The purpose of this article is to show that the distribution of the longest fragment in the random multisection problem after k steps and the height of m-ary search trees (and some extensions) are not only closely related in a formal way but both can be asymptotically described with the same distribution function that has to be shifted in a proper way (travelling wave). The crucial property for the proof is a so-called intersection property that transfers inequalities between two distribution functions (resp. of their Laplace transforms) from one level to the next. It is conjectured that such intersection properties hold in a much more general context. If this property is verified convergence to a travelling wave follows almost automatically.
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Chauvin, B., Drmota, M. The Random Multisection Problem, Travelling Waves and the Distribution of the Height of m-Ary Search Trees. Algorithmica 46, 299–327 (2006). https://doi.org/10.1007/s00453-006-0107-7
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DOI: https://doi.org/10.1007/s00453-006-0107-7