English

Entropy rates for Horton self-similar trees

Discrete Mathematics 2018-05-24 v2 Combinatorics

Abstract

In this paper we examine planted binary plane trees. First, we provide an exact formula for the number of planted binary trees with given Horton-Strahler orders. Then, using the notion of entropy, we examine the structural complexity of random planted binary trees with N vertices. Finally, we quantify the complexity of the tree's structural properties as tree grows in size, by evaluating the entropy rate for planted binary plane trees with N vertices and for planted binary plane trees that satisfy Horton Law with Horton exponent R.

Keywords

Cite

@article{arxiv.1804.06989,
  title  = {Entropy rates for Horton self-similar trees},
  author = {Evgenia V. Chunikhina},
  journal= {arXiv preprint arXiv:1804.06989},
  year   = {2018}
}