Self affine tiling and Pisot numeration system. (English) Zbl 0999.11065

Kanemitsu, Shigeru (ed.) et al., Number theory and its applications. Proceedings of the conference held at the RIMS, Kyoto, Japan, November 10-14, 1997. Dordrecht: Kluwer Academic Publishers. Dev. Math. 2, 7-17 (1999).
The author studies tilings of a Euclidean space, generated by means of Pisot numbers. It is proved that if a Pisot number is a unit, and satisfies a finite expansibility property, then the origin is an inner point of the corresponding central tile. Under an additional condition, the tiles are shown to be arcwise connected.
For the entire collection see [Zbl 0932.00040].


11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)