Enumerative combinatorics
European Journal of Combinatorics
Some Combinatorial Properties of Schubert Polynomials
Journal of Algebraic Combinatorics: An International Journal
Key polynomials and a flagged Littlewood-Richardson rule
Journal of Combinatorial Theory Series A
Planar decompositions of tableaux and Schur function determinants
European Journal of Combinatorics
Lattice path proofs for determinantal formulas for symplectic and orthogonal characters
Journal of Combinatorial Theory Series A
The Flagged Double Schur Function
Journal of Algebraic Combinatorics: An International Journal
Transformations of Border Strips and Schur Function Determinants
Journal of Algebraic Combinatorics: An International Journal
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We obtain a tableau definition of the skew Schubert polynomials named by Lascoux, which are defined as flagged double skew Schur functions. These polynomials are in fact Schubert polynomials in two sets of variables indexed by 321-avoiding permutations. From the divided difference definition of the skew Schubert polynomials, we construct a lattice path interpretation based on the Chen-Li-Louck pairing lemma. The lattice path explanation immediately leads to the determinantal definition and the tableau definition of the skew Schubert polynomials. For the case of a single variable set, the skew Schubert polynomials reduce to flagged skew Schur functions as studied by Wachs and by Billey, Jockusch, and Stanley. We also present a lattice path interpretation for the isobaric divided difference operators, and derive an expression of the flagged Schur function in terms of isobaric operators acting on a monomial. Moreover, we find lattice path interpretations for the Giambelli identity and the Lascoux-Pragacz identity for super-Schur functions. For the super-Lascoux-Pragacz identity, the lattice path construction is related to the code of the partition which determines the directions of the lines parallel to the y-axis in the lattice.