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Primitive substitutive numbers are closed under rational multiplication

Pallavi KetkarLuca Q. Zamboni — 1998

Journal de théorie des nombres de Bordeaux

Let M ( r ) denote the set of real numbers α whose base- r digit expansion is ultimately primitive substitutive, i.e., contains a tail which is the image (under a letter to letter morphism) of a fixed point of a primitive substitution. We show that the set M ( r ) is closed under multiplication by rational numbers, but not closed under addition.

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