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Advancing in the presence of a demon. (English) Zbl 1174.05008

Summary: We study a parameter that contains approximate counting, i.e., the level reached after \(n\) random increments, driven by geometric probabilities, and insertion costs for tries as special cases. We are able to compute all moments of this parameter in a semi-automatic fashion. This is another showcase of the machinery developed in an earlier paper of these authors. Roughly speaking, it works when the underlying distributions are distributed according to the Gumbel distribution, or something similar.

MSC:

05A16 Asymptotic enumeration
68P05 Data structures
68R05 Combinatorics in computer science
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