New two-line arrays representing partitions (Q659639)

By representing a number as a vector and providing a representation of this vector as a sum of vectors, the authors present combinatorial interpretations for sums into two parameters, from which they obtain, as special cases, combinatorial interpretations of several partitions identities. These includes Rogers-Ramanujan identities, unrestricted partitions, and Lebesgue's partition identity. Two-line matrices are also used to provide combinatorial interpretations in some particular cases.