40 citations · 178 across the 39 of their papers we have counts for
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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…
Esthetic Numbers and Lifting Restrictions on the Analysis of Summatory Functions of Regular Sequences
Clemens Heuberger, Daniel Krenn
When asymptotically analysing the summatory function of a -regular sequence in the sense of Allouche and Shallit, the eigenvalues of the sum of matrices of the linear representa…
Reducing Simply Generated Trees by Iterative Leaf Cutting
Benjamin Hackl, Clemens Heuberger, Stephan Wagner
We consider a procedure to reduce simply generated trees by iteratively removing all leaves. In the context of this reduction, we study the number of vertices that are deleted afte…
Analysis of Summatory Functions of Regular Sequences: Transducer and Pascal's Rhombus
Clemens Heuberger, Daniel Krenn, Helmut Prodinger
The summatory function of a -regular sequence in the sense of Allouche and Shallit is analysed asymptotically. The result is a sum of periodic fluctuations for eigenvalues of ab…
Ascents in Non-Negative Lattice Paths
Benjamin Hackl, Clemens Heuberger, Helmut Prodinger
Non-negative Łukasiewicz paths are special two-dimensional lattice paths never passing below their starting altitude which have only one single special type of down step. They are…