A refined bijection between alternating permutations and 0-1-2 increasing trees

preprint2010arXivOpen access

We construct a refined bijection $ϕ$ between alternating permutations and 0-1-2 increasing trees with degree at most 2. It satisfies that the first element of alternating permutation $π$ is equal to the first vertex in $ϕ(π)$ in the postorder.

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A refined bijection between alternating permutations and 0-1-2 increasing trees

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