14 citations · 33 across the 30 of their papers we have counts for
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An example of an automatic sequence with non-regular abelian complexity
Jean-Paul Allouche, Narad Rampersad, Michel Rigo +2
Answering a question of Madill and Rampersad, we give an example a of a -automatic sequence whose abelian complexity is not -regular.
Effective Computation of Generalized Abelian Complexity for Pisot Type Substitutive Sequences
Jean-Michel Couvreur, Martin Delacourt, Nicolas Ollinger +3
Generalized abelian equivalence compares words by their factors up to a certain bounded length. The associated complexity function counts the equivalence classes for factors of a g…
Magic numbers in periodic sequences
Savinien Kreczman, Luca Prigioniero, Eric Rowland +1
In formal languages and automata theory, the magic number problem can be formulated as follows: for a given integer n, is it possible to find a number d in the range [n,2^n] such t…
Revisiting regular sequences in light of rational base numeration systems
Michel Rigo, Manon Stipulanti
Regular sequences generalize the extensively studied automatic sequences. Let be an abstract numeration system. When the numeration language is prefix-closed and regular, a…
Automatic sequences: from rational bases to trees
Michel Rigo, Manon Stipulanti
The th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of in a suitable numeration system. In this paper, instead…
Cobham's Theorem and Automaticity
Lucas Mol, Narad Rampersad, Jeffrey Shallit +1
We make certain bounds in Krebs' proof of Cobham's theorem explicit and obtain corresponding upper bounds on the length of a common prefix of an aperiodic -automatic sequence an…