English

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

R2 v1 2026-06-22T04:51:29.092Z