Reductions of Binary Trees and Lattice Paths induced by the Register Function
Abstract
The register function (or Horton-Strahler number) of a binary tree is a well-known combinatorial parameter. We study a reduction procedure for binary trees which offers a new interpretation for the register function as the maximal number of reductions that can be applied to a given tree. In particular, the precise asymptotic behavior of the number of certain substructures ("branches") that occur when reducing a tree repeatedly is determined. In the same manner we introduce a reduction for simple two-dimensional lattice paths from which a complexity measure similar to the register function can be derived. We analyze this quantity, as well as the (cumulative) size of an (iteratively) reduced lattice path asymptotically.
Keywords
Cite
@article{arxiv.1612.07286,
title = {Reductions of Binary Trees and Lattice Paths induced by the Register Function},
author = {Benjamin Hackl and Clemens Heuberger and Helmut Prodinger},
journal= {arXiv preprint arXiv:1612.07286},
year = {2017}
}
Comments
Full version of the extended abstract arXiv:1602.06200