Counting ternary trees according to the number of middle edges and factorizing into $(3/2)$-ary trees
Combinatorics
2020-09-16 v1
Abstract
The sequence A120986 in the Encyclopedia of Integer Sequences counts ternary trees according to the number of nodes and the number of middle edges. Using a certain substition, the underlying cubic equation can be factored. This leads to an extension of the concept of -ary trees, introduced by Knuth in his christmas lecture from 2014.
Cite
@article{arxiv.2009.06793,
title = {Counting ternary trees according to the number of middle edges and factorizing into $(3/2)$-ary trees},
author = {Helmut Prodinger},
journal= {arXiv preprint arXiv:2009.06793},
year = {2020}
}
Comments
Plans are to extend this material, if possible. Comments are welcome