Walks on tiled boards
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929281543700480 |
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| author | Németh, László |
| author_facet | Németh, László |
| contents | Several articles deal with tilings with various shapes, and also a very frequent type of combinatorics is to examine the walks on graphs or on grids. We combine these two things and give the numbers of the shortest walks crossing the tiled $(1\times n)$ and $(2\times n)$ square grids by covering them with squares and dominoes. We describe these numbers not only recursively, but also as rational polynomial linear combinations of Fibonacci numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12159 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Walks on tiled boards Németh, László Combinatorics Number Theory 11B37, 05C38, 52C20, 11Y55 Several articles deal with tilings with various shapes, and also a very frequent type of combinatorics is to examine the walks on graphs or on grids. We combine these two things and give the numbers of the shortest walks crossing the tiled $(1\times n)$ and $(2\times n)$ square grids by covering them with squares and dominoes. We describe these numbers not only recursively, but also as rational polynomial linear combinations of Fibonacci numbers. |
| title | Walks on tiled boards |
| topic | Combinatorics Number Theory 11B37, 05C38, 52C20, 11Y55 |
| url | https://arxiv.org/abs/2403.12159 |