Morphisms, Symbolic Sequences, and Their Standard Forms
F. Michel Dekking
Delft University of Technology
2628 CD Delft
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.
Full version: pdf,
(Concerned with sequences
Received August 31 2015; revised version received December 7 2015.
Published in Journal of Integer Sequences, December 16 2015.
Journal of Integer Sequences home page