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Decomposition theorem for invertible substitutions on three-letter alphabet

B. Tan·Z. -X. Wen·Y. -P. Zhang
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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.

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B. Tan, Z. -X. Wen, Y. -P. Zhang. 2002-10-17. Decomposition theorem for invertible substitutions on three-letter alphabet. https://arxiv.org/abs/math/0210262

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