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Abstract The aim of this paper is to study the connection between different properties related to β-expansions. In particular, the relation between two conditions, both ensuring purely discrete spectrum of the odometer, is analyzed. The first one is the so-called Hypothesis B for the G-odometers and the second one is denoted by (QM) and it has been introduced in the framework of tilings associated to Pisot β-numerations.

Linear Recursive Odometers and Beta-Expansions