The register function for lattice paths

Abstract

The register function for binary trees is the minimal number of extra registers required to evaluate the tree. This concept is also known as Horton-Strahler numbers. We extend this definition to lattice paths, built from steps $\pm 1$, without positivity restriction. Exact expressions are derived for appropriate generating functions. A procedure is presented how to get asymptotics of all moments, in an almost automatic way; this is based on an earlier paper of the authors.

Keywords

• register function
• horton-strahler numbers
• gumbel distribution
• moments
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-ds] mathematics [math]/dynamical systems [math.ds]
• [math.math-co] mathematics [math]/combinatorics [math.co]