Decomposition theorem for invertible substitutions on threeletter alphabet
Abstract
We shall characterize the structure of invertible substitutions on threeletter alphabet. We show that any invertible substitution, after some cyclic operation, can be written as a finite product of permutations and Fibonacci's substitution. As a consequence, a matrix (of order 3 and with nonnegative integral coefficients) is the matrix of an invertible substitution if and only if it is a finite product of nonnegative elementary matrices.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2002
 DOI:
 10.48550/arXiv.math/0210262
 arXiv:
 arXiv:math/0210262
 Bibcode:
 2002math.....10262T
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Combinatorics;
 20M05;
 68R15
 EPrint:
 18 pages,pdf