Generating Trees and Fibonacci Polyominoes

2024/11/26 by Juan F. Pulido, Pulido, Juan F., José L. Ramírez +3 · 1 voice · 1 citation
Mathematics · #math.CO

paper · pdf · doi:10.48550/arxiv.2411.17812

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.

Cited by

• Irregularity and Topological Indices in Fibonacci Word Trees and Modified Fibonacci Word Index

Discussions

• New paper on arxiv (arxiv.org/abs/2411.17812)! Joint work with Juan F. Pulido and José L. Ramírez from 🇨🇴. We study a new class of polyominoes, called p-Fibonacci polyominoes, defined using p-Fibona [bsky, 15 points, 0 comments]

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