Williams’s conjecture is false for reducible subshifts
Williams’s conjecture is false for reducible subshifts
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 <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-bracket upper W right-bracket"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>W</mml:mtext> </mml:mrow> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">[{\text …