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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The commuting block maps problem


Authors: Ethan M. Coven, G. A. Hedlund and Frank Rhodes
Journal: Trans. Amer. Math. Soc. 249 (1979), 113-138
MSC: Primary 54H20
DOI: https://doi.org/10.1090/S0002-9947-1979-0526313-4
MathSciNet review: 526313
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Abstract: A block map is a map $ f:\,{\{ {\text{0}},\,{\text{1}}\} ^n}\, \to \,\{ 0,\,1\} $ for some $ n\, \geqslant \,1$. A block map f induces an endomorphism $ {f_\infty }$ of the full 2-shift $ (X,\,\sigma )$. We define composition of block maps so that $ {(f \circ g)_\infty }\, = \,{f_\infty } \circ {g_\infty }$. The commuting block maps problem (for f) is to determine $ \mathcal{C}(f)\, = \,\{ g\vert f \circ g\, = \,g \circ f\} $. We solve the commuting block maps problem for a number of classes of block maps.


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DOI: https://doi.org/10.1090/S0002-9947-1979-0526313-4
Article copyright: © Copyright 1979 American Mathematical Society