Geodesic
Symmetric Polyomino Tilings, Tribones, Ideals, and Gröbner Bases
Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 1
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We apply the theory of Gröbner bases to the study of signed, symmetric polyomino tilings of planar domains. Complementing the results of Conway and Lagarias we show that the triangular regions $T_N=T_{3k-1}$ and $T_N=T_{3k}$ in a hexagonal lattice admit a \emph{signed tiling} by three-in-line polyominoes (tribones) \emph{symmetric} with respect to the $120^{\circ}$ rotation of the triangle if and only if either $N=27r-1$ or $N=27r$ for some integer $r\geq 0$. The method applied is quite general and can be adapted to a large class of symmetric tiling problems.
DOI : 10.2298/PIM1512001M
Classification : 52C20, 13P10
Keywords: signed polyomino tilings, Gröbner bases, tessellations 
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     title = {Symmetric {Polyomino} {Tilings,} {Tribones,} {Ideals,} and {Gr\"obner} {Bases}},
     journal = {Publications de l'Institut Math\'ematique},
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Manuela Muzika Dizdarević; Rade T. Živaljević. Symmetric Polyomino Tilings, Tribones, Ideals, and Gröbner Bases. Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 1 . doi: 10.2298/PIM1512001M

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