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Journal of the American Mathematical Society

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Williams's conjecture is false for reducible subshifts


Authors: K. H. Kim and F. W. Roush
Journal: J. Amer. Math. Soc. 5 (1992), 213-215
MSC: Primary 54H20; Secondary 15A36, 28D20
DOI: https://doi.org/10.1090/S0894-0347-1992-1130528-4
MathSciNet review: 1130528
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Abstract: We show that for two subshifts of finite type having exactly two irreducible components, strong shift equivalence is not the same as shift equivalence. This refutes the Williams conjecture $ [{\text{W}}]$ in the reducible case. The irreducible case remains an open problem.


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Additional Information

DOI: https://doi.org/10.1090/S0894-0347-1992-1130528-4
Keywords: Strong shift equivalence, shift equivalence, reducible shift, subshift of finite type
Article copyright: © Copyright 1992 American Mathematical Society