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Bijections on Rooted Trees with Fixed Size of Maximal Decreasing Subtrees

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Abstract

Recently, Seo and Shin showed that the number of rooted trees on [n + 1] = 1, 2, . . . , n+1 such that the maximal decreasing subtree with the same root has k + 1 vertices is equal to the number of functions f : [n] → [n] such that the image of f contains [k]. We give a bijective proof of this theorem.

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  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Jang Soo Kim

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  1. Jang Soo Kim
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Correspondence to Jang Soo Kim.

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Kim, J.S. Bijections on Rooted Trees with Fixed Size of Maximal Decreasing Subtrees. Ann. Comb. 17, 339–352 (2013). https://doi.org/10.1007/s00026-013-0182-9

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  • DOI: https://doi.org/10.1007/s00026-013-0182-9

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