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Transactions of the American Mathematical Society

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

 
 

 

The sums of powers theorem for commuting block maps


Author: Frank Rhodes
Journal: Trans. Amer. Math. Soc. 271 (1982), 225-236
MSC: Primary 54H20; Secondary 58F11
DOI: https://doi.org/10.1090/S0002-9947-1982-0648088-0
MathSciNet review: 648088
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Abstract: A block map is a map $ f:{\{ 0,\,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 )$. Composition of block maps is defined in such a way that $ {(f \circ g)_\infty } = {f_\infty } \circ {g_\infty }$. In this paper some recent results concerning the set $ \{ g\vert g \circ f = f \circ g\} $ for certain types of block maps $ f$ are extended.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0648088-0
Article copyright: © Copyright 1982 American Mathematical Society

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