A seminal technique of theoretical physics (e.g. Wick's theorem) interprets the Gaussian matrix integral of the products of the trace of powers of Hermitian matrices as the number of labelled maps with a given degree sequence, sorted by their Euler characteristics. This leads to the map enumeration results analogous to those obtained by combinatorial methods.
We show that the enumeration of the graphs embeddable on a given 2-dimensional surface can also be formulated by the Gaussian matrix integral of an ice-type partition function. We also express the number of the graphs with a fixed directed cycle double cover as the Gaussian matrix integral of an Ihara-Selberg-type function.
We show that the enumeration of the graphs embeddable on a given 2-dimensional surface can also be formulated by the Gaussian matrix integral of an ice-type partition function. We also express the number of the graphs with a fixed directed cycle double cover as the Gaussian matrix integral of an Ihara-Selberg-type function.
