Substitutions over infinite alphabet generating (−β)-integers

This contribution is devoted to the study of positional numeration systems with negative base introduced by Ito and Sadahiro in 2009, called (−β)-expansions. We give an admissibility criterion for more general case of (−β)-expansions and discuss the properties of the set of (−β)-integers. We give a description of distances within this set and show that this set can be coded by an infinite word over an infinite alphabet, which is a fixed point of a non-erasing non-trivial morphism.