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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
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.

References [Enhancements On Off] (What's this?)

  • [1] Ethan M. Coven, G. A. Hedlund and Frank Rhodes, The commuting block maps problem, Trans. Amer. Math. Soc. 249 (1979), 113-138. MR 526313 (81k:54072)
  • [2] G. A Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory 3 (1969), 320-375. MR 41 #4510. MR 0259881 (41:4510)

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Article copyright: © Copyright 1982 American Mathematical Society

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