Expansions and tilings

Charlene Kalle (Universiteit Utrecht)

Number expansions can be obtained from iterations of certain transformations. For example, the transformation Tx = \beta x (mod 1) generates expansions of elements in the interval [0,1) in base \beta and with integers between 0 and the floor of \beta as digits. If \beta is a certain kind of algebraic integer, then this transformation is linked to a tiling of a Euclidean space. Properties of the number expansions can be obtained from the tiling and vice versa. We will discuss the construction of this tiling in a specific and famous example and, if time permits, consider generalizations to a larger class of expansion generating transformations.

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