Generating Trees and Fibonacci Polyominoes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915036361916416 |
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| author | Pulido, Juan F. Ramírez, José L. Vindas-Meléndez, Andrés R. |
| author_facet | Pulido, Juan F. Ramírez, José L. Vindas-Meléndez, Andrés R. |
| contents | We study a new class of polyominoes, called $p$-Fibonacci polyominoes, defined using $p$-Fibonacci words. We enumerate these polyominoes by applying generating functions to capture geometric parameters such as area, semi-perimeter, and the number of inner points. Additionally, we establish bijections between Fibonacci polyominoes, binary Fibonacci words, and integer compositions with certain restrictions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17812 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generating Trees and Fibonacci Polyominoes Pulido, Juan F. Ramírez, José L. Vindas-Meléndez, Andrés R. Combinatorics 05A15, 05A05, 11B39 We study a new class of polyominoes, called $p$-Fibonacci polyominoes, defined using $p$-Fibonacci words. We enumerate these polyominoes by applying generating functions to capture geometric parameters such as area, semi-perimeter, and the number of inner points. Additionally, we establish bijections between Fibonacci polyominoes, binary Fibonacci words, and integer compositions with certain restrictions. |
| title | Generating Trees and Fibonacci Polyominoes |
| topic | Combinatorics 05A15, 05A05, 11B39 |
| url | https://arxiv.org/abs/2411.17812 |