The structure of invertible substitutions on a three-letter alphabet |
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| Authors: | Bo Tan Zhi-Xiong Wen Yiping Zhang |
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| Institution: | Department of Mathematics, Wuhan University, 430072 Hubei, Wuhan, PR China |
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| Abstract: | We study the structure of invertible substitutions on three-letter alphabet. We show that there exists a finite set
of invertible substitutions such that any invertible substitution can be written as Iwσ1σ2σk, where Iw is the inner automorphism associated with w, and
for 1jk. 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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| Keywords: | Invertible substitution Indecomposable substitution Combinatorics of words |
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