Grand zigzag knight's paths - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Grand zigzag knight's paths

Résumé

We study the enumeration of different classes of grand knight's paths in the plane. In particular, we focus on the subsets of zigzag knight's paths that are subject to constraints. These constraints include ending at $y$-coordinate 0, bounded by a horizontal line, confined within a tube, among other considerations. We present our results using generating functions or direct closed-form expressions. We derive asymptotic results, finding approximations for quantities such as the probability that a zigzag knight's path stays in some area of the plane, or for the average of the altitude of such a path. Additionally, we exhibit some bijections between grand zigzag knight's paths and some pairs of compositions.
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Dates et versions

hal-04460988 , version 1 (25-10-2024)

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Jean-Luc Baril, Nathanaël Hassler, Sergey Kirgizov, José L. Ramírez. Grand zigzag knight's paths. 2024. ⟨hal-04460988⟩
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