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# Tiling the Line with Triples

Abstract : It is known the one dimensional prototile $0,a,a+b$ and its reflection $0,b,a+b$ always tile some interval. The subject has not received a great deal of further attention, although many interesting questions exist. All the information about tilings can be encoded in a finite digraph $D_{ab}$. We present several results about cycles and other structures in this graph. A number of conjectures and open problems are given. In [Go] an elegant proof by contradiction shows that a greedy algorithm will produce an interval tiling. We show that the process of converting to a direct proof leads to much stronger results.
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Conference papers
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Cited literature [2 references]

https://hal.inria.fr/hal-01182962
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Submitted on : Thursday, August 6, 2015 - 10:44:49 AM
Last modification on : Tuesday, March 7, 2017 - 3:00:24 PM
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### File

dmAA0119.pdf
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### Citation

Aaron Meyerowitz. Tiling the Line with Triples. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. pp.257-274, ⟨10.46298/dmtcs.2282⟩. ⟨hal-01182962⟩

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