Abstract
We study the structure of invertible substitutions on three-letter alphabet. We show that there exists a finite set S of invertible substitutions such that any invertible substitution can be written as I w ∘ σ 1∘ σ 2∘⋯∘ σ k , where I w is the inner automorphism associated with w, and σ j∈ S for 1⩽ j⩽ k. As a consequence, M is the matrix of an invertible substitution if and only if it is a finite product of non-negative elementary matrices.
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