The Commuting Block Maps Problem

A block map is a map $f: \{0, 1\}^n \rightarrow \{0, 1\}$ for some $n \leqslant 1$. 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...

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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
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Summary:A block map is a map $f: \{0, 1\}^n \rightarrow \{0, 1\}$ for some $n \leqslant 1$. 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 $\mathscr{C}(f) = \{g|f \circ g = g \circ f\}$. 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