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math.CO2025
Asymptotic Analysis of Regular Sequences
Clemens Heuberger, Daniel Krenn
In this article, -regular sequences in the sense of Allouche and Shallit are analysed asymptotically. It is shown that the summatory function of a regular sequence can asymptoti…
math.CO2024
The distribution of the maximum protection number in simply generated trees
Clemens Heuberger, Sarah J. Selkirk, Stephan Wagner
The protection number of a vertex in a tree is the length of the shortest path from to any leaf contained in the maximal subtree where is the root. In this paper, we de…
math.CO2024
Analysis of Regular Sequences: Summatory Functions and Divide-and-Conquer Recurrences
Clemens Heuberger, Daniel Krenn, Tobias Lechner
In the asymptotic analysis of regular sequences as defined by Allouche and Shallit, it is usually advisable to study their summatory function because the original sequence has a to…