nLab Pólya enumeration theorem

Idea

The Pólya enumeration theorem is a particular theorem in enumerative combinatorics; it serves as a basis of methods often called Pólya’s enumeration (counting) theory. It is especially used in counting of graphs, including often in applications like chemistry.

The Pólya “theory” can be redone in terms of Joyal’s species.

References

• wikipedia Pólya enumeration theorem

• G. Pólya, R. C. Read, Combinatorial enumeration of groups, graphs, and chemical compounds, Springer-Verlag

The theory can also be rederived from state sum identities in certain positive TQFTs:

• Markus Banagl, Positive topological quantum field theories, Quantum Topology 6 4 (2015) 609-706 [arxiv/1303.4276, doi:10.4171/qt/71]

category: combinatorics