English

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.

Keywords

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