Juan B. Gil, Felix H. Xu, William Y. Zhu
Published 2025-06-18Version 1
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.
Comments: 16 pages. Accepted for publication
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