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.
Publié le : 2001-07-04
Classification:
Tiling,
one dimension,
direct proof,
[INFO]Computer Science [cs],
[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG],
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
@article{hal-01182962,
author = {Meyerowitz, Aaron},
title = {Tiling the Line with Triples},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01182962}
}
Meyerowitz, Aaron. Tiling the Line with Triples. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-01182962/