Bi-partite ribbon graphs arise in organising the large $N$ expansion of
correlators in random matrix models and in the enumeration of observables in
random tensor models. There is an algebra $\cK(n)$, with basis given by
bi-partite ribbon graphs with $n$ edges, which is useful in the applications to
matrix and tensor models. The algebra $ \cK(n)$ is closely related to symmetric
group algebras and has a matrix-block decomposition related to Clebsch-Gordan
multiplicities, also known as Kronecker coefficients, for symmetric group
representations. Quantum mechanical models which use $\cK(n)$ as Hilbert spaces
can be used to give combinatorial algorithms for computing the Kronecker
coefficients.
