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 pre...

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Vydané v:Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings vol. AA,...; číslo Proceedings; s. 257 - 274
Hlavný autor: Meyerowitz, Aaron
Médium: Journal Article Konferenčný príspevok..
Jazyk:English
Vydavateľské údaje: DMTCS 01.01.2001
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Edícia:DMTCS Proceedings
Predmet:
[info.info-cg] computer science [cs]/computational geometry [cs.cg]
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[info] computer science [cs]
[math.math-co] mathematics [math]/combinatorics [math.co]
Combinatorics
Computational Geometry
Computer Science
direct proof
Discrete Mathematics
Mathematics
one dimension
tiling
one dimension
direct proof
Tiling
ISSN:1365-8050, 1462-7264, 1365-8050
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Popis
Shrnutí: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.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2282