Reconstruction of low degree domino tilings
β Scribed by Andrea Frosini; Simi Giulia
- Book ID
- 104444358
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 148 KB
- Volume
- 12
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
β¦ Synopsis
We want to present a new way of challenging the classical and still unsolved problem of the reconstruction of a domino tiling from its horizontal and vertical projections. We introduce the concept of degree of a domino tiling, i.e. we divide a domino tiling into strips-like sub-tilings and we consider the greatest of their heights. We propose an algorithm which generalizes some known strategies for reconstructing domino tilings of degree two, to tilings of degree lesser or equal four.
π SIMILAR VOLUMES
Let t(k, n) denote the number of ways to tile a C x n rectangle with 1 x 2 rectangles (called dominoes). We show that for each fixed k the s( quence tk = (t(k, O), t(k, I), . . .) satisfies a difference equation (linear, homogeneous, and w ith constant coefficients). Furthermore, a computational met
The classical cosine formula for enumerating domino tilings of a rectangle, due to Kasteleyn, Temperley, and Fisher, is proved once again, here using a combination of standard tools from combinatorics and algebra.
We consider the problem of tiling with dominoes pictures of the plane. in theoretical and algorithmic aspects. For generalities and other tiling problems, see for example Refs. Beauquier et al. (1995), Conway and Lagarias (1990). Kannan and Soroker (1992), Kenyon (1992), and Beauquier (1991). The pi