Document Type
Article
Department
Mathematics (HMC)
Publication Date
4-14-2011
Abstract
We consider regular tessellations of the plane as infinite graphs in which q edges and q faces meet at each vertex, and in which p edges and p vertices surround each face. For 1/p + 1/q = 1/2, these are tilings of the Euclidean plane; for 1/p + 1/q < 1/2, they are tilings of the hyperbolic plane. We choose a vertex as the origin, and classify vertices into generations according to their distance (as measured by the number of edges in a shortest path) from the origin. For all p ≥ 3 and q ≥ 3 with 1/p + 1/q ≤ 1/2, we give simple combinatorial derivations of the rational generating functions for the number of vertices in each generation.
Rights Information
© 2011 American Mathematical Society
Recommended Citation
Paul A., and Pippenger N. “A Census of Vertices by Generations in Regular Tessellations of the Plane”, Electronic Journal of Combinatorics, 18, 87 (2011).
Comments
First published in the Electronic Journal of Combinatorics in 2011, published by the American Mathematical Society.