On ranked and bounded Kohnert posets

TL;DR

This paper investigates the combinatorial structure of Kohnert posets, providing conditions for when they are bounded and ranked, with applications to Demazure characters, advancing understanding of their properties.

Contribution

It offers new criteria for boundedness and ranking of Kohnert posets, including complete characterizations in special cases like Demazure characters.

Findings

Identified sufficient conditions for boundedness of Kohnert posets.

Established necessary conditions for their ranking.

Provided complete characterizations in special cases such as Demazure characters.

Abstract

In this paper, we explore combinatorial properties of the posets associated with Kohnert polynomials. In particular, we determine a sufficient condition guaranteeing when such ``Kohnert posets'' are bounded and two necessary conditions for when they are ranked. Moreover, we apply the aforementioned conditions to find complete characterizations of when Kohnert posets are bounded and when they are ranked in special cases, including those associated with Demazure characters.