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 wσ 1σ ...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 wσ 1σ 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.展开更多
文摘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 wσ 1σ 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.
