  Alternating sign matrices are known to be equinumerous with descending plane
partitions, totally symmetric self-complementary plane partitions and
alternating sign triangles, but no bijective proof for any of these
equivalences has been found so far. In this paper we provide the first
bijective proof of the operator formula for monotone triangles, which has been
the main tool for several non-combinatorial proofs of such equivalences. In
this proof, signed sets and sijections (signed bijections) play a fundamental
role.
