Bijections on rooted trees with fixed size of maximal decreasing subtrees

Jang Soo Kim

Bijections on rooted trees with fixed size of maximal decreasing subtrees

Combinatorics 2011-08-31 v1

Authors: Jang Soo Kim

Abstract

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

Keywords

rooted trees maximal decreasing subtree bijection functions combinatorial proof

Cite

@article{arxiv.1108.6038,
  title  = {Bijections on rooted trees with fixed size of maximal decreasing subtrees},
  author = {Jang Soo Kim},
  journal= {arXiv preprint arXiv:1108.6038},
  year   = {2011}
}

Comments

9 pages

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