Exact enumeration of fullerenes
Geometric Topology
2024-06-17 v3 Combinatorics
Abstract
A fullerene, or buckyball, is a trivalent graph on the sphere with only pentagonal and hexagonal faces. Building on ideas of Thurston, we use modular forms to give an exact formula for the number of oriented fullerenes with a given number of vertices.
Cite
@article{arxiv.2304.01655,
title = {Exact enumeration of fullerenes},
author = {Philip Engel and Jan Goedgebeur and Peter Smillie},
journal= {arXiv preprint arXiv:2304.01655},
year = {2024}
}
Comments
Minor corrections and improvements. 31 pages, 3 figures. Appendix by Jan Goedgebeur