Kohnert Posets and Polynomials of Northeast Diagrams

Kohnert polynomials and their associated posets are combinatorial objects with deep geometric and representation theoretic connections, generalizing both Schubert polynomials and type-A Demazure characters. In this paper, we explore the properties of Kohnert polynomials indexed by northeast diagrams along with their associated posets. We give separate classifications of the bounded, ranked, and multiplicity-free Kohnert posets for northeast diagrams, each of which can be computed in polynomial time with respect to the number of cells in the diagram. As an initial application, we specialize these classifications to simple criteria in the case of lock diagrams.