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arXiv · 2506.15800

Odd-indexed Fibonacci numbers via pattern-avoiding permutations

Juan B. Gil·Felix H. Xu·William Y. Zhu
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Abstract

In this paper, we consider several combinatorial problems whose enumeration leads to the odd-indexed Fibonacci numbers, including certain types of Dyck paths, block fountains, directed column-convex polyominoes, and set partitions with no crossings and no nestings. Our goal is to provide bijective maps to pattern-avoiding permutations and derive generating functions that track certain positional statistics at the permutation level.

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Juan B. Gil, Felix H. Xu, William Y. Zhu. 2025-06-18. Odd-indexed Fibonacci numbers via pattern-avoiding permutations. https://doi.org/10.5281/zenodo.17144254

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