Substitutions over infinite alphabet generating (-β)-integers

Abstract

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.

In Proceedings WORDS 2011, arXiv:1108.3412