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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
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…
math.CO2024
Asymptotic Analysis of q-Recursive Sequences
Clemens Heuberger, Daniel Krenn, Gabriel F. Lipnik
For an integer , a -recursive sequence is defined by recurrence relations on subsequences of indices modulo some powers of~. In this article, -recursive sequences a…