[en] Let I be a finite set of integers and F be a finite set of maps of the form n->k_i n + l_i with integer coefficients. For an integer base k>=2, we study the k-recognizability of the minimal set X of integers containing I and satisfying f(X)\subseteq X for all f in F. In particular, solving a conjecture of Allouche, Shallit and Skordev, we show under some technical conditions that if two of the constants k_i are multiplicatively independent, then X is not k-recognizable for any k>=2.
Disciplines :
Mathematics Computer science
Author, co-author :
Kärki, Tomi
Lacroix, Anne ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
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