Enumeration of paths in a hexagonal circle packing
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.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Stochastic processes and statistical mechanics
Random Matrices and Applications
Publication details
- Journal / source
- Discrete Mathematics
- Volume
- 349
- Issue
- 9
- Pages
- 115194–115194
- Publication date
- 4 May 2026
- Language
- EN