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Odd-indexed Fibonacci numbers via pattern-avoiding permutations (2506.15800v1)
Published 18 Jun 2025 in math.CO
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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