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We show the equivalence of the Pieri formula for flag manifolds and certainidentities among the structure constants, giving new proofs of both the Pieriformula and of these identities. A key step is the association of a symmetricfunction to a finite poset with labeled Hasse diagram satisfying a symmetrycondition. This gives a unified definition of skew Schur functions, Stanleysymmetric function, and skew Schubert functions (defined here). We also usealgebraic geometry to show the coefficient of a monomial in a Schubertpolynomial counts certain chains in the Bruhat order, obtaining a newcombinatorial construction of Schubert polynomials.Comment: 24 pages, LaTeX 2e, with epsf.st

Skew Schubert functions and the Pieri formula for flag manifolds