# 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.
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Roesler, Uwe. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, pp.135-148, 2008, DMTCS Proceedings
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https://hal.inria.fr/hal-01194675
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• HAL Id : hal-01194675, version 1

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Guy Louchard, Helmut Prodinger. The register function for lattice paths. Roesler, Uwe. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, pp.135-148, 2008, DMTCS Proceedings. 〈hal-01194675〉

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