On the enumeration of Hoppy's walks
Helmut Prodinger
TL;DR
This paper improves the enumeration formula for k-Dyck paths ending at a specific level after a certain number of steps, with a focus on paths ending with an up-step.
Contribution
It provides an improved sum formula for counting k-Dyck paths ending at level j after m up-steps, refining previous results by Deng and Mansour.
Findings
Derived a new sum formula for k-Dyck path enumeration
Enhanced the accuracy of counting paths ending at a specific level
Built upon and improved previous enumeration formulas
Abstract
The enumeration of k-Dyck paths ending at level j after m up-steps, where the last step is an up-step, is given as a sum, improving on a previous formula given by Deng and Mansour.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Computational Geometry and Mesh Generation · Mathematical Dynamics and Fractals