Partially strict shifted plane partitions (Q1262314)

For a pair (A,B) of complementary subsets of positive integers, an (A,B) partially strict shifted plane partition is a shifted partition \(\sigma =(a_{ij})_{i\leq j},\quad (a_{ij}\geq a_{ij+1}\) and \(a_{ij}\geq a_{i+1j})\) such that (1) for any \(m\in A\), m appears at most once in each row, and (2) for any \(m\in B\), m appears at most once in each column. In this article the author obtains a generating function for them by using a ``lattice path'' method. This yields generating function for row-strict (resp. column-strict) shifted plane partitions, which is a determinantal formula in terms of elementary (resp. complete) symmetric polynomials. A weighted generating function for monotone triangles is also derived.