Enumeration of paths in a hexagonal circle packing

2025/11/17 by Baril, Jean-Luc, rez, José Luis Ramí
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.13446

Abstract

We investigate paths in the hexagonal circle packing and enumerate them with respect to width, height, number of steps, area, and kissing number. Functional equations and the kernel method yield closed bivariate generating functions together with coefficient formulas and asymptotics. We establish bijections with skew Dyck paths, constrained Motzkin paths, and peakless Motzkin paths, and show that several of the associated counting arrays are Riordan arrays. Continued-fraction expansions for the area and kissing-number enumerators are also obtained.

Citations

• A walk in my lattice path garden
• Partial skew Dyck paths -- a kernel method approach

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