Kohnert posets and polynomials of northeast diagrams

TL;DR

This paper studies Kohnert polynomials and their posets associated with northeast diagrams, providing classifications and polynomial-time algorithms for key properties, with applications to lock diagrams.

Contribution

It offers new classifications and polynomial-time algorithms for properties of Kohnert posets related to northeast diagrams, advancing combinatorial understanding.

Findings

Classified bounded, ranked, and multiplicity-free Kohnert posets for northeast diagrams.

Provided polynomial-time algorithms to compute these classifications.

Applied classifications to derive simple criteria for lock diagrams.

Abstract

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 and their posets indexed by northeast diagrams. 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.