Morphisms, Symbolic Sequences, and Their Standard Forms

Title

Morphisms, Symbolic Sequences, and Their Standard Forms

 Author

Dekking, F.M.

Faculty

Electrical Engineering, Mathematics and Computer Science

 Department

Delft Institute of Applied Mathematics

 Date

2016-01-31

 Abstract

Morphisms are homomorphisms under the concatenation operation of the set of words over a finite alphabet. Changing the elements of the finite alphabet does not change the morphism in an essential way. We propose a method to select a unique representative from 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, such as The On-Line Encyclopedia of Integer Sequences. We illustrate our proposals with the k-symbol Fibonacci sequences.

 To reference this document use:

http://resolver.tudelft.nl/uuid:f5ed2a58-400e-4cd3-bcc2-4c803c985daf

 Publisher

University of Waterloo

 ISSN

1530-7638

 Source

Journal of Integer Sequences, 19 (1), 2016

 Part of collection

Institutional Repository

 Document type

journal article

 Rights

(c) 2016 Dekking, F.M.
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