Bijections on rooted trees with fixed size of maximal decreasing subtrees

Details Bijections on rooted trees with fixed size of maximal decreasing subtrees Bijections on rooted trees with fixed size of maximal decreasing subtrees

2011-08-30

arxiv.org/abs/1108.6038v1

Mathematics

Combinatorics

9 pages

Scientific paper

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.

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