Odd-indexed Fibonacci numbers via pattern-avoiding permutations
Combinatorics
2026-03-24 v1
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.
Cite
@article{arxiv.2506.15800,
title = {Odd-indexed Fibonacci numbers via pattern-avoiding permutations},
author = {Juan B. Gil and Felix H. Xu and William Y. Zhu},
journal= {arXiv preprint arXiv:2506.15800},
year = {2026}
}
Comments
16 pages. Accepted for publication