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1 Florida Atlantic University Boca Raton

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.

Keywords : Tiling one dimension direct proof

Author: Aaron Meyerowitz -

Source: https://hal.archives-ouvertes.fr/


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