Particle Seas and Basic Hypergeometric Series

The author introduces overpartitions and particle seas as a generalization of partitions. Both new tools are used in bijective proofs of basic hypergeometric identities like the q-binomial theorem, Jacobi’s triple product, q-Gauß equality or even Ramanujan’s 1Ψ1 summation. 1. Partitions In 1969, G. E. Andrews was already looking for bijective proofs for some basic hypergeometric identities. The principle of bijective proofs is simple: if each side of an equation can be construed as a generating function counting some parameters for sets A and B of combinatorial objects, and we can go bijectively between objects of the two sets transforming the parameters on objects from A into the parameters of objects from B, then we have an identity. Let us first recall the notation