Signed shape tilings of squares
Abstract
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 \Qweighted tiles with the same shape as T, and necessary and sufficient conditions for a square to be tilable by finitely many \Zweighted 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 1998
 DOI:
 10.48550/arXiv.math/9809118
 arXiv:
 arXiv:math/9809118
 Bibcode:
 1998math......9118K
 Keywords:

 Mathematics  Combinatorics;
 52C20
 EPrint:
 LaTeX, 14 pages, to appear in Discrete Mathematics. This version differs from the original only cosmetically