Tilings by Translation: Enumeration by a Rational Language Approach

Beauquier and Nivat introduced and gave a characterization of the class of pseudo-square polyominoes that tile the plane by translation: a polyomino tiles the plane by translation if and only if its boundary word W may be factorized as W = XY X Y . In this paper we consider the subclass PSP of pseudo-square polyominoes which are also parallelogram. By using the Beauquier-Nivat characterization we provide by means of a rational language the enumeration of the subclass of psp-polyominoes with a fixed planar basis according to the semi-perimeter. The case of pseudo-square convex polyominoes is also analyzed.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Srecko Brlek, Andrea Frosini, Simone Rinaldi, Laurent Vuillon
• Keywords: Boundary Word, COMBINATORICS 2006, Polyominoes, Pseudo-square Polyominoes