Asymptotic properties of free monoid morphisms [article]

Emilie Charlier, Julien Leroy, Michel Rigo
2016 arXiv   pre-print
Motivated by applications in the theory of numeration systems and recognizable sets of integers, this paper deals with morphic words when erasing morphisms are taken into account. Cobham showed that if an infinite word w =g(f^ω(a)) is the image of a fixed point of a morphism f under another morphism g, then there exist a non-erasing morphism σ and a coding τ such that w =τ(σ^ω(b)). Based on the Perron theorem about asymptotic properties of powers of non-negative matrices, our main contribution
more » ... s an in-depth study of the growth type of iterated morphisms when one replaces erasing morphisms with non-erasing ones. We also explicitly provide an algorithm computing σ and τ from f and g.
arXiv:1507.00206v2 fatcat:w73clccturgb3p4l6smnypdlua