A sign-reversing involution to count labeled lone-child-avoiding trees
Combinatorics
2014-07-01 v1
Abstract
We use a sign-reversing involution to show that trees on the vertex set [n], considered to be rooted at 1, in which no vertex has exactly one child are counted by 1/n sum_{k=1}^{n} (-1)^(n-k) {n}-choose-{k} (n-1)!/(k-1)! k^(k-1). This result corrects a persistent misprint in the Encyclopedia of Integer Sequences.
Keywords
Cite
@article{arxiv.1406.7784,
title = {A sign-reversing involution to count labeled lone-child-avoiding trees},
author = {David Callan},
journal= {arXiv preprint arXiv:1406.7784},
year = {2014}
}
Comments
4 pages