Christoffel and fibonacci tiles

Abstract

Among the polyominoes that tile the plane by translation, the so-called squares have been conjectured to tile the plane in at most two distinct ways (these are called double squares). In this paper, we study two families of tiles : one is directly linked to Christoffel words while the other stems from the Fibonacci sequence. We show that these polyominoes are double squares, revealing strong connections between discrete geometry and other areas by means of combinatorics on words. © 2009 Springer Berlin Heidelberg.