The Proportion of Trees that are Linear
Combinatorics
2020-03-23 v2
Abstract
We study several enumeration problems connected to linear trees, a broad class which includes stars, paths, generalized stars, and caterpillars. We provide generating functions for counting the number of linear trees on vertices, characterize the asymptotic growth rate of the number of nonisomorphic linear trees, and show that the distribution of -linear trees on vertices follows a central limit theorem.
Keywords
Cite
@article{arxiv.1901.08502,
title = {The Proportion of Trees that are Linear},
author = {Tanay Wakhare and Eric Wityk and Charles R. Johnson},
journal= {arXiv preprint arXiv:1901.08502},
year = {2020}
}
Comments
8 pages; v2 contains new central limit theorem, as suggested by the referee