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arXiv · 1509.00260

Morphisms, Symbolic sequences, and their Standard Forms

F. Michel Dekking
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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 $k$-symbol Fibonacci sequences.

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F. Michel Dekking. 2016-01-13. Morphisms, Symbolic sequences, and their Standard Forms. https://arxiv.org/abs/1509.00260

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