TL;DR
This paper investigates the amplitude of Motzkin paths, a parameter related to twice the height, using generating functions to analyze its properties.
Contribution
It introduces a detailed analysis of the amplitude of Motzkin paths through generating functions, providing new insights into this recently introduced parameter.
Findings
Derived generating function expressions for the amplitude
Calculated asymptotic behavior of the amplitude
Provided combinatorial interpretations of the results
Abstract
The amplitude of Motzkin paths was recently introduced, which is basically twice the height. We analyze this parameter using generating functions.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Geometric and Algebraic Topology · Stochastic processes and statistical mechanics