On PP-partitions related to ordinal sums of posets

Using the inclusion–exclusion principle, we derive a formula of generating functions for PP-partitions related to ordinal sums of posets. This formula simplifies computations for many variations of plane partitions, such as plane partition polygons and plane partitions with diagonals or double diagonals. We illustrate our method by several examples, some of which are new variations of plane partitions.