Signed shape tilings of squares

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Let T be a tile in the Cartesian plane made up of finitely many rectangles whose corners have rational coordinates and whose sides are parallel to the coordinate axes. This paper gives necessary and sufficient conditions for a square to be tilable by finitely many \Q-weighted tiles with the same shape as T, and necessary and sufficient conditions for a square to be tilable by finitely many \Z-weighted tiles with the same shape as T. The main tool we use is a variant of F. W. Barnes's algebraic theory of brick packing, which converts tiling problems into problems in commutative algebra.
LaTeX, 14 pages, to appear in Discrete Mathematics. This version differs from the original only cosmetically

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Combinatorics, 52C20

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http://salesiana.dossiersoluciones.com/handle/123456789/77424

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9809118
 http://arxiv.org/abs/math/9809118

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arXiv