Abstract
In this chapter we explain the connection between coloring results from combinatorics and topological dynamical systems, an aspect that was discovered by Furstenberg and Weiss. Since their seminal paper (Furstenberg and Weiss 1978b) a new area has emerged that has been an active field of research ever since.
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Notes
- 1.
Color is my day-long obsession, joy and torment.
- 2.
Encyclopédie Larousse: Claude Monet.
- 3.
The terminology “IP” may refer to “Infinite Parallelepiped.” In fact, \(\mathop{\mathrm{FS}}(n_{k}) =\{ n_{1},n_{2},n_{1} + n_{2},n_{3},n_{1} + n_{3},n_{2} + n_{3},n_{1} + n_{2} + n_{3},\ldots \}\) resembles an infinite parallelepiped.
- 4.
P.J.H. Baudet (1891–1921), Professor of Pure and Applied Mathematics and Mechanics at the Technische Hogeschool te Delft
- 5.
According to some authors the terminology IP set refers to IdemPotents.
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© 2015 Tanja Eisner, Bálint Farkas, Markus Haase, and Rainer Nagel
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Eisner, T., Farkas, B., Haase, M., Nagel, R. (2015). Topological Dynamics and Colorings. In: Operator Theoretic Aspects of Ergodic Theory. Graduate Texts in Mathematics, vol 272. Springer, Cham. https://doi.org/10.1007/978-3-319-16898-2_19
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