The commuting block maps problem

A block map is a map f:{0,1}n→{0,1}f:\,{\{ {\text {0}},\,{\text {1}}\} ^n}\, \to \,\{ 0,\,1\} for some n⩾1n\, \geqslant \,1. A block map f induces an endomorphism f∞{f_\infty } of the full 2-shift (X,σ)(X,\,\sigma ). We define composition of block maps so that (f∘g)∞=f∞∘g∞{(f \circ g)_\infty }\, = \...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 1979, Vol.249 (1), p.113-138
Main Authors: Coven, Ethan M., Hedlund, G. A., Rhodes, Frank
Format: Article
Language:English
Subjects:
Coefficients
Commuting
Covens
Integers
Mathematical functions
Mathematical rings
Mathematical sets
Odd numbers
Polynomials
Research article
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Summary:A block map is a map f:{0,1}n→{0,1}f:\,{\{ {\text {0}},\,{\text {1}}\} ^n}\, \to \,\{ 0,\,1\} for some n⩾1n\, \geqslant \,1. A block map f induces an endomorphism f∞{f_\infty } of the full 2-shift (X,σ)(X,\,\sigma ). We define composition of block maps so that (f∘g)∞=f∞∘g∞{(f \circ g)_\infty }\, = \,{f_\infty } \circ {g_\infty }. The commuting block maps problem (for f) is to determine C(f)={g|f∘g=g∘f}\mathcal {C}(f)\, = \,\{ g|f \circ g\, = \,g \circ f\}. We solve the commuting block maps problem for a number of classes of block maps.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-1979-0526313-4