Publications de l'Institut Mathématique, Nouvelle Série Vol. 98(112), pp. 1–23 (2015) 

Symmetric polyomino tilings, tribones, ideals, and Gröbner basesManuela Muzika Dizdarevic, Rade T. ZivaljevicFaculty of Natural Sciences and Mathematics, Sarajevo, Bosnia and Herzegovina; Mathematical Institute SASA, Belgrade, SerbiaAbstract: 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 $T_N=T_{3k1}$ and $T_N=T_{3k}$ in a hexagonal lattice admit a \emph{signed tiling} by threeinline polyominoes (tribones) \emph{symmetric} with respect to the $120^{\circ}$ rotation of the triangle if and only if either $N=27r1$ 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. Keywords: signed polyomino tilings; Gröbner bases; tessellations Classification (MSC2000): 52C20; 13P10 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 18 Nov 2015. This page was last modified: 6 Jan 2016.
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