Planar decompositions of tableaux and Schur function determinants

Abstract In this paper we describe planar decompositions of skew shape tableaux into strips and use the shapes of these strips to generate a determinant. We then prove that each of these determinants is equal to the Schur function for the skew shape. The Jacobi-Trudi identity, the dual Jacobi-Trudi identity, the Giambelli identity and the rim ribbon identity of Lascoux and Pragacz are all special cases of this theorem. A compact Gessel-Viennot lattice path argument provides the proof.