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The structure of invertible substitutions on a three-letter alphabet

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Analysis in Theory and Applications

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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Authors and Affiliations

  1. Department of Mathematics, Wuhan University, 430072, Wuhan, Hubei, P. R. China

    Tan Bo, Wen Zhixiong & Zhang Yiping

Authors
  1. Tan Bo
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  2. Wen Zhixiong
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  3. Zhang Yiping
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Correspondence to Tan Bo.

Additional information

This paper was presented in the Fractal Satellite Conference of ICM 2002 in Najing.

Research supported by NSFC and by the Special Funds for Major State Basic Research Projects of China.

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Bo, T., Zhixiong, W. & Yiping, Z. The structure of invertible substitutions on a three-letter alphabet. Anal. Theory Appl. 19, 365–382 (2003). https://doi.org/10.1007/BF02835535

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  • DOI: https://doi.org/10.1007/BF02835535

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