Substitutions over infinite alphabet generating (-β)-integers

Details Substitutions over infinite alphabet generating (-β)-integers Substitutions over infinite alphabet generating (-β)-integers

2011-08-18

arxiv.org/abs/1108.3627v1

EPTCS 63, 2011, pp. 115-121

Computer Science

Discrete Mathematics

In Proceedings WORDS 2011, arXiv:1108.3412

Scientific paper

10.4204/EPTCS.63.16

This contribution is devoted to the study of positional numeration systems with negative base introduced by Ito and Sadahiro in 2009, called (-\beta)-expansions. We give an admissibility criterion for more general case of (-\beta)-expansions and discuss the properties of the set of (-\beta)-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.

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