On ranked and bounded Kohnert posets

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.