\Gamma
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by Kevin Keating, Jonathan L. King
http://www.combinatorics.org/Volume_4/PostScriptfiles/v4i2r12.ps
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Abstract:
Abstract. Given a list 1\Theta1; 1\Thetaa; 1\Thetab; : : : ; 1\Thetac of rectangles, with a; b; : : : ; c non-negative, when can 1 \Theta t be tiled by positive and negative copies of rectangles which are similar (uniform scaling) to those in the list? We prove that such a tiling exists iff t is in the field Q(a; b; : : : ; c). When can rectangle 1 \Theta t be packed by (finitely many) squares? Dehn1903 gave the answer: If and only if t is rational. For irrational t he showed 1 \Theta t not packable by means of what we will call a "Dehn-functional". It is a map D from pairs of real numbers to R (or any abelian group) which satisfies: D
Citations
| 76 | Topics in Algebra – HERSTEIN - 1964 |
| 8 | Tiling and Monotone Boolean Functions, Preprint available at: http://www.math.ufl .edu/squash/tilingstuff.html – King, Brick - 1998 |
| 5 | Tilings of the Square with Similar Rectangles, Discrete Comput – Laczkovich, Szekeres - 1995 |
| 4 | die Zerlegung von Rechtecken in Rechtecke – Dehn - 1903 |
| 4 | Tiling a Square with Similar Rectangles – Rinne - 1994 |
