Quivers and partition identities

Hall polynomials count short exact sequences in Fq-linear categories.
For categories of quiver representations, they can be expressed in terms of Gaussian polynomials (also known as q-binomial coefficients). Many statements in tilting theory and the theory of Hall algebras are therefore equivalent to basic hypergeometric identities. I will show how such statements, which have been proved by homological methods, can be used to give bijective proofs of certain partition identities.