53 citations · 146 across the 35 of their papers we have counts for
10 papers · 1 filter
Decidability of uniform recurrence of morphic sequences
Fabien Durand
We prove that the uniform recurrence of morphic sequences is decidable. For this we show that the number of derived sequences of uniformly recurrent morphic sequences is bounded. A…
HD0L--equivalence and periodicity problems in the primitive case (to the memory of G. Rauzy)
Fabien Durand
In this paper I would like to witness the mathematical inventiveness of G. Rauzy through personnal exchanges I had with him. The objects that will emerge will be used to treat the…
Decidability of the HD0L ultimate periodicity problem
Fabien Durand
In this paper we prove the decidability of the HD0L ultimate periodicity problem.
Multidimensional extension of the Morse--Hedlund theorem
Fabien Durand, Michel Rigo
A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence over a finite alphabet is ultimately periodic if and only if, for some , the number of diff…
Cobham's theorem for substitutions
Fabien Durand
The seminal theorem of Cobham has given rise during the last 40 years to a lot of works around non-standard numeration systems and has been extended to many contexts. In this paper…
Syndeticity and independent substitutions
Fabien Durand, Michel Rigo
We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we define the no…