Abstract
We study the structure of invertible substitutions on three-letter alphabet. We show that there exists a finite setS of invertible substitutions such that any invertible substitution can be written asI w∘σ1∘σ2∘...∘σk, 3 where Iw is the inner automorphism associated with w, and σj∈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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