10 citations · 74 across the 27 of their papers we have counts for
29 papers
Probabilistic analysis of optimal multi-pivot QuickSort
Cecilia Holmgren, Jasper Ischebeck, Daniel Krenn +2
We consider a multi-pivot QuickSort algorithm using pivot elements to partition a nonsorted list into sublists in order to proceed recursively on these subli…
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…
Strongly k-recursive sequences
Daniel Krenn, Jeffrey Shallit
Drawing inspiration from a recent paper of Heuberger, Krenn, and Lipnik, we define the class of strongly k-recursive sequences. We show that every k-automatic sequence is strongly…
A Note on the Relation between Recognisable Series and Regular Sequences, and their Minimal Linear Representations
Clemens Heuberger, Daniel Krenn, Gabriel F. Lipnik
In this note, we precisely elaborate the connection between recognisable series (in the sense of Berstel and Reutenauer) and -regular sequences (in the sense of Allouche and Sha…
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…
A characterization of graphs with regular distance- graphs
Elisabeth Gaar, Daniel Krenn
For non-negative integers~, we consider graphs in which every vertex has exactly vertices at distance~, i.e., graphs whose distance- graphs are -regular. We call su…