DMTCS Proceedings, Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001

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Tiling the Line with Triples

Aaron Meyerowitz


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 Dab. We present several results about cycles and other structures in this graph. A number of conjectures and open problems are given.

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