On the Recognizability of Self-generating Sets
نویسندگان
چکیده
Let I be a finite set of integers and F be a finite set of maps of the form n 7→ ki n + `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 φ(X) ⊆ X for all φ ∈ F . In particular, solving a conjecture of Allouche, Shallit and Skordev, we show under some technical conditions that if two of the constants ki are multiplicatively independent, then X is not k-recognizable for any k ≥ 2.
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