Tilings by translation: enumeration by a rational language approach
The electronic journal of combinatorics, Tome 13 (2006)
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.
@article{10_37236_1041,
author = {Srecko Brlek and Andrea Frosini and Simone Rinaldi and Laurent Vuillon},
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/}
}
TY - JOUR AU - Srecko Brlek AU - Andrea Frosini AU - Simone Rinaldi AU - Laurent Vuillon TI - Tilings by translation: enumeration by a rational language approach JO - The electronic journal of combinatorics PY - 2006 VL - 13 UR - http://geodesic.mathdoc.fr/articles/10.37236/1041/ DO - 10.37236/1041 ID - 10_37236_1041 ER -
%0 Journal Article %A Srecko Brlek %A Andrea Frosini %A Simone Rinaldi %A Laurent Vuillon %T Tilings by translation: enumeration by a rational language approach %J The electronic journal of combinatorics %D 2006 %V 13 %U http://geodesic.mathdoc.fr/articles/10.37236/1041/ %R 10.37236/1041 %F 10_37236_1041
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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