Abstract
For a subset D of boxes in an n×n square grid, let χD(x) denote the dual character of the flagged Weyl module associated to D. It is known that χD(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 χD(x). Mészáros, St. Dizier and Tanjaya conjectured that χD(x) attains the upper bound if and only if D avoids a certain single subdiagram. We provide a proof of this conjecture.
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