Peter Paule, RISC, J. Kepler University, Linz, Austria

Short and Easy Computer Proofs of Partition and $q$-Identities

Many partition identities in additive number theory can be stated as limiting cases of $q$-hypergeometric summation identities. Recent progress concerning the algorithmic treatment of $q$-hypergeometric sums is discussed. The applications include, for instance, a simple ``four-line'' computer proof of the celebrated Rogers-Ramanujan identities.