Alternating sign matrices (ASMs) were introduced by Robbins and Rumsey in the early 1980s. Together with Mills they conjectured an enumerative formula for the number of ASMs of size n x n, which was proved independently by Zeilberger and Kuperberg about 10 years later. In this talk, I will present the first bijective proof of this result. A crucial part is played by signed sets and sijections (bijections on signed sets).

This is a joint project with Ilse Fischer.