eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2001-01-01
DMTCS Proceedings vol. AA,...
Proceedings
10.46298/dmtcs.2282
2282
journal article
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 $D_{ab}$. 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.
https://dmtcs.episciences.org/2282/pdf
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]