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arXiv · 2411.17812

Generating Trees and Fibonacci Polyominoes

Juan F. Pulido·José L. Ramírez·Andrés R. Vindas-Meléndez
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Abstract

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.

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Juan F. Pulido, José L. Ramírez, Andrés R. Vindas-Meléndez. 2024-11-26. Generating Trees and Fibonacci Polyominoes. https://arxiv.org/abs/2411.17812

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