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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Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings vol. AA,...; no. Proceedings; pp. 257 - 274
Main Author: Meyerowitz, Aaron
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 01.01.2001
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Series:DMTCS Proceedings
Subjects:
[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
Online Access:Get full text
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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.
AbstractList 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.
Author Meyerowitz, Aaron
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  organization: Florida Atlantic University [Boca Raton]
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Keywords one dimension
direct proof
Tiling
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SubjectTerms [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
Title Tiling the Line with Triples
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