Dominance Method for Plane Partitions. \(V\): Enumeration of Ladder Tableaux

The concept of ladder tableaux is introduced, which may be considered as a natural extension of the shifted tableaux. By means of the dominance technique, a pair of determinantal expressions in terms of symmetric functions, for the generating function of ladder tableaux with a fixed shape, is established. As applications, the particular cases yield the generating functions for column-strict reverse plane partitions, symmetrical reverse plane partitions, and column-strict shifted reverse plane partitions with a given shape and with no part-restrictions.