The symmetric functions catalog

An overview of symmetric functions and related topics


Kohnert polynomials

Kohnert polynomials were introduced by Assaf and Searles in [AS22b]. This is a large family of polynomials, which contains several of the classical families as special cases, in particular the family of Schubert polynomials and key polynomials.

All Kohnert polynomials are monomial slide positive, [Thm. 3.7, AS22b], and they were later proved to be key positive in [Ass21].

See [AABE23] for a representation-theoretical interpretation of Kohnert polynomials.