Williams’s conjecture is false for reducible subshifts

Kim, K. H.; Roush, F. W.

doi:10.1090/S0894-0347-1992-1130528-4

Williams’s conjecture is false for reducible subshifts
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by K. H. Kim and F. W. Roush

J. Amer. Math. Soc. 5 (1992), 213-215

DOI: https://doi.org/10.1090/S0894-0347-1992-1130528-4

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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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