N. Bergeron and F. Sottile. Skew Schubert functions and the Pieri formula for flag manifolds. Trans. Amer. Math. Soc., 354:651--673, 2002.

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A Unified Approach to Combinatorial Formulas for Schubert.. - Lenart   (Correct)

.... tableaux [15, 16, 13] Section 4) Kohnert diagrams [11, 26, 27] Section 5) and balanced labelings of the diagram of a permutation [6] Section 6) We do not mention here the construction of Schubert polynomials in terms of certain increasing labeled chains in Bruhat order on the symmetric group [3]; the connection between these chains and rc graphs is explored in [18] The main tools in our investigation are certain operations on rc graphs, which correspond to the coplactic operations on tableaux, and thus define a crystal graph structure on rc graphs. A new definition of these operations ....

N. Bergeron and F. Sottile. Skew Schubert functions and the Pieri formula for flag manifolds. Trans. Amer. Math. Soc., 354:651--673, 2002.

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