[en] The concept of k-automatic sequences is at the intersection of number theory and formal language theory. It has been generalized by the notion of k-regularity that allows to study sequences with values in a (possibly infinite) ring. This concept provides us with structural information about how the different terms of the sequence are related to each other.
They are many different notions related to the measure of complexity of an infinite sequence w. A classical approach is its factor complexity. In an abelian context, the analogue to the factor complexity is the abelian complexity where the number of distinct factors of length n is counted up to abelian equivalence. The notion of abelian complexity was extended to that of l-abelian complexity.
In this talk, I propose to use tools from the wavelet theory to analyze the l-abelian complexity. For the numerical simulations, I apply the wavelet leaders method that allows to study the pointwise regularity of signals.
Disciplines :
Mathematics
Author, co-author :
Kleyntssens, Thomas ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Nicolay, Samuel ; Université de Liège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Vandomme, Elise ; Université de Liège > Département de mathématique > Mathématiques discrètes
Rigo, Michel ; Université de Liège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Use of the wavelet theory as a tool to investigate the l-abelian complexity of a sequence
