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COMBINATORICS
2006

Tilings by Translation: Enumeration by a Rational Language Approach

8 years 11 months ago
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.
Srecko Brlek, Andrea Frosini, Simone Rinaldi, Laur
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where COMBINATORICS
Authors Srecko Brlek, Andrea Frosini, Simone Rinaldi, Laurent Vuillon
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