Exact enumeration of fullerenes
arXiv:2304.01655
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.
Minor corrections and improvements. 31 pages, 3 figures. Appendix by Jan Goedgebeur