Geodesic
The register function for lattice paths
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science (2008).

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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. 
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     author = {Louchard, Guy and Prodinger, Helmut},
     title = {The register function for lattice paths},
     journal = {Discrete mathematics & theoretical computer science},
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Louchard, Guy; Prodinger, Helmut. The register function for lattice paths. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science (2008). doi : 10.46298/dmtcs.3560. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3560/

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