For a subset D of boxes in an nΓn square grid, let ΟDβ(x)
denote the dual character of the flagged Weyl module associated to D. It is
known that ΟDβ(x) specifies to a Schubert polynomial (resp., a key
polynomial) in the case when D is the Rothe diagram of a permutation (resp.,
the skyline diagram of a composition). One can naturally define a lower and an
upper bound of ΟDβ(x). M{\'e}sz{\'a}ros, St. Dizier and Tanjaya
conjectured that ΟDβ(x) attains the upper bound if and only if D
avoids a certain subdiagram. We provide a proof of this conjecture