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Tiling the line with translates of one tile
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lagarias, Jeffrey C. Wang, Yang |
| Copyright Year | 1998 |
| Abstract | A region T is a closed subset of the real line of positive finite Lebesgue measure which has a boundary of measure zero. Call a region T a tile if R can be tiled by measure-disjoint translates of T. For a bounded tile all tilings of R with its translates are periodic, and there are finitely many translationequivalence classes of such tilings. The main result of the paper is that for any tiling of R by a bounded tile, any two tiles in the tiling differ by a rational multiple of the minimal period of the tiling. From it we a structure theorem characterizing such tiles in terms of complementing sets for finite cyclic groups. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://users.math.msu.edu/users/ywang/Reprints/tiling-1d-inv.pdf |
| Alternate Webpage(s) | http://www.math.ust.hk/~yangwang/Reprints/tiling-1d-inv.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Class Subgroup Tiling window manager |
| Content Type | Text |
| Resource Type | Article |
