Linear recursive odometers and beta-expansions

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 pure discrete spectrum of the odometer, is analysed. 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.

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