Geodesic
Tilings by translation: enumeration by a rational language approach
The electronic journal of combinatorics, Tome 13 (2006)

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Zbl EuDML
Beauquier and Nivat introduced and gave a characterization of the class of pseudo-square polyominoes, i.e. those 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 $W = XY\overline{X} \,\overline{Y}$. 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.
DOI : 10.37236/1041
Classification : 05A15, 05B45, 05B50
Mots-clés : polyominoes 
Srecko Brlek; Andrea Frosini; Simone Rinaldi; Laurent Vuillon. Tilings by translation: enumeration by a rational language approach. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1041
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     title = {Tilings by translation: enumeration by a rational language approach},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1041},
     zbl = {1081.05007},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1041/}
}
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