  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.
