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## The Williams conjecture is false for irreducible subshifts

### K. H. Kim and F. W. Roush

**Abstract.**
We prove that the Williams conjecture is false for irreducible subshifts of finite type using relative
sign-gyration numbers defined between different subshifts.

*Copyright 1997 American Mathematical Society*

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#### Article Info

- ERA Amer. Math. Soc.
**03** (1997), pp. 105-109
- Publisher Identifier: S 1079-6762(97)00032-2
- 1991
*Mathematics Subject Classification*. Primary 58F03, 54H20
*Key words and phrases*. Williams conjecture, irreducible
subshift of finite type, strong shift equivalence,
gyration numbers
- Received by the editors June 5, 1997
- Posted on October 16, 1997
- Communicated by Svetlana Katok
- Accompanying program (Maple)

**K. H. Kim**

Mathematics Research Group, Alabama State University, Montgomery,
AL 36101-0271, and Korean Academy of Science and Technology

*E-mail address:* `kkim@asu.alasu.edu`

**F. W. Roush**

Mathematics Research Group, Alabama State University, Montgomery,
AL 36101-027

*E-mail address:* `froush@asu.alasu.edu`

The authors were partially supported by NSF Grants DMS 9024813
and DMS 9405004.

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