Name
Abstract | ||
|---|---|---|
This paper proves a conjecture of Thurston on tiling a certain triangular region T 3 N + 1 of the hexagonal lattice with three-in-line (“tribone”) tiles. It asserts that for all packings of T 3 N + 1 with tribones leaving exactly one uncovered cell, the uncovered cell must be the central cell. Furthermore there are exactly 2 N such packings. This exact counting result is analogous to closed formulae for the number of allowable configurations in certain exactly solved models in statistical mechanics, and implies that the configurational entropy (per site) of tiling T 3 N + 1 with tribones with one defect tends to 0 as N → ∞. |
Year | DOI | Venue |
|---|---|---|
1993 | 10.1016/0097-3165(93)90065-G | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
configurational entropy,polyomino tiling problem | Hexagonal lattice,Discrete mathematics,Combinatorics,Rhombille tiling,Trihexagonal tiling,Lattice path,Hexagonal tiling,Polyomino,Configuration entropy,Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
63 | 2 | Journal of Combinatorial Theory, Series A |
Citations | PageRank | References |
9 | 1.68 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| J. C. Lagarias | 1 | 563 | 235.61 |
| D. S. Romano | 2 | 9 | 2.01 |