On the density of intermediate β-shifts of finite type

Abstract

We determine the structure of the set of intermediate $β$-shifts of finite type. Specifically, we show that this set is dense in the parameter space $Δ= \{ (β, α) \in \mathbb{R}^{2} \colon β\in (1, 2) \; \text{and} \; 0 \leq α\leq 2 - β\}$. This generalises the classical result of Parry from 1960 for greedy and (normalised) lazy $β$-shifts.

6 pages