Geodesic
Shape tiling
The electronic journal of combinatorics, The Wilf Festschrift volume, Tome 4 (1997) no. 2
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Given a list $1\times 1, 1\times a, 1\times b, \dots, 1\times c$ of rectangles, with $a,b,\dots,c$ non-negative, when can $1\times{t}$ 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 $Q(a,b,\dots,c)$.
DOI : 10.37236/1327
Classification : 05B45, 52C20, 51M25, 05B50, 12E99 
@article{10_37236_1327,
     author = {Kevin Keating and Jonathan L. King},
     title = {Shape tiling},
     journal = {The electronic journal of combinatorics},
     year = {1997},
     volume = {4},
     number = {2},
     doi = {10.37236/1327},
     zbl = {0885.05055},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1327/}
}
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Kevin Keating; Jonathan L. King. Shape tiling. The electronic journal of combinatorics, The Wilf Festschrift volume, Tome 4 (1997) no. 2. doi: 10.37236/1327

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