{"docId":2282,"paperId":2282,"url":"https:\/\/dmtcs.episciences.org\/2282","doi":"10.46298\/dmtcs.2282","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":246,"name":"DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)"}],"section":[{"sid":66,"title":"Proceedings","description":[]}],"repositoryName":"Hal","repositoryIdentifier":"hal-01182962","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-01182962v1","dateSubmitted":"2016-11-21 15:43:14","dateAccepted":null,"datePublished":"2001-01-01 00:00:00","titles":{"en":"Tiling the Line with Triples"},"authors":["Meyerowitz, Aaron"],"abstracts":{"en":"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."},"keywords":[["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]"]}