Parallelogram Tilings and Jacobi-Perron Algorithm

Parallelogram Tilings, Worms, and Finite Orientations

This paper studies properties of tilings of the plane by parallelograms. In particular it is established that in parallelogram tilings using a finite number of shapes all tiles occur in only finitely many orientations.

On the Singularization of the Two-Dimensional Jacobi-Perron Algorithm

2000 AMS Subject Classification: Primary 11K50

Arithmetic distributions of convergents arising from Jacobi-Perron algorithm

We study the distribution modulo m of the convergents associated with the d-dimensional Jacobi-Perron algorithm for a.e. real numbers in (0, 1) by proving the ergodicity of a skew product of the Jacobi-Perron transformation; this skew product was initially introdued in [6] for regular continued fractions.

The two-dimensional Jacobi-Perron Algorithm is S-equivalent to the Podsypanin Algorithm

We show that the two-dimensional Podsypanin Algorithm and the two-dimensional Jacobi-Perron Algorithm belong to the same class of Sexpansions. In particular, we show that each step of the conversion process described in Schratzberger 2007 [16], based on the techniques of Singularization and Insertion, terminates after finitely many states a.e.

A class of transcendental numbers with explicit g - adic expansion and the Jacobi – Perron algorithm