2019/01/24 by Wakhare, Tanay, Wityk, Eric, Johnson, Charles R.
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1901.08502
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 n vertices, characterize the asymptotic growth rate of the number of nonisomorphic linear trees, and show that the distribution of k-linear trees on n vertices follows a central limit theorem.