10.46298/dmtcs.2282
https://dmtcs.episciences.org/2282
Meyerowitz, Aaron
Aaron
Meyerowitz
Tiling the Line with Triples
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.
episciences.org
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]
2023-01-30
2001-01-01
2001-01-01
en
journal article
https://hal.science/hal-01182962v1
1365-8050
https://dmtcs.episciences.org/2282/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)
Proceedings
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