Generating Trees and Fibonacci Polyominoes
Combinatorics
2024-11-28 v1
Abstract
We study a new class of polyominoes, called -Fibonacci polyominoes, defined using -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.
Cite
@article{arxiv.2411.17812,
title = {Generating Trees and Fibonacci Polyominoes},
author = {Juan F. Pulido and José L. Ramírez and Andrés R. Vindas-Meléndez},
journal= {arXiv preprint arXiv:2411.17812},
year = {2024}
}
Comments
14 pages, 8 figures, comments are welcomed