Decomposition theorem for invertible substitutions on three-letter alphabet
Group Theory
2007-05-23 v1 Combinatorics
Abstract
We shall characterize the structure of invertible substitutions on three-letter 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 non-negative integral coefficients) is the matrix of an invertible substitution if and only if it is a finite product of non-negative elementary matrices.
Cite
@article{arxiv.math/0210262,
title = {Decomposition theorem for invertible substitutions on three-letter alphabet},
author = {B. Tan and Z. -X. Wen and Y. -P. Zhang},
journal= {arXiv preprint arXiv:math/0210262},
year = {2007}
}
Comments
18 pages,pdf