Isoperimetric Formulas for Hyperbolic Animals
Combinatorics
2022-07-01 v1
Abstract
An animal is a planar shape formed by attaching congruent regular polygons along their edges. In 1976, Harary and Harborth gave closed isoperimetric formulas for Euclidean animals. Here, we provide analogous formulas for hyperbolic animals. We do this by proving a connection between Sturmian words and the parameters of a discrete analogue of balls in the graph determined by hyperbolic tessellations. This reveals a complexity in hyperbolic animals that is not present in Euclidean animals.
Keywords
Cite
@article{arxiv.2206.14910,
title = {Isoperimetric Formulas for Hyperbolic Animals},
author = {Erika Roldan and Rosemberg Toala-Enriquez},
journal= {arXiv preprint arXiv:2206.14910},
year = {2022}
}
Comments
16 pages, 2 figures, 3 tables