English

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.

Keywords

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

R2 v1 2026-07-22T16:48:30.319Z