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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Cori, Robert and Mazoyer, Jacques and Morvan, Michel and Mosseri, Rémy. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), pp.257-274, 2001, DMTCS Proceedings
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Aaron Meyerowitz. Tiling the Line with Triples. Cori, Robert and Mazoyer, Jacques and Morvan, Michel and Mosseri, Rémy. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), pp.257-274, 2001, DMTCS Proceedings. 〈hal-01182962〉

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