Morphisms, Symbolic sequences, and their Standard Forms
Combinatorics
2016-01-14 v2 Formal Languages and Automata Theory
Abstract
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member out of all these morphisms. This has applications to the classification of the shift dynamical systems generated by morphisms. In a similar way, we propose the selection of a representing sequence out of the class of symbolic sequences over an alphabet of fixed cardinality. Both methods are useful for the storing of symbolic sequences in databases, like The On-Line Encyclopedia of Integer Sequences. We illustrate our proposals with the -symbol Fibonacci sequences.
Cite
@article{arxiv.1509.00260,
title = {Morphisms, Symbolic sequences, and their Standard Forms},
author = {F. Michel Dekking},
journal= {arXiv preprint arXiv:1509.00260},
year = {2016}
}