A Pieri Rule for Skew Shapes
Journal of Combinatorial Theory (Series A)
The Pieri rule expresses the product of a Schur function and a single row Schur function in terms of Schur functions. We extend the classical Pieri rule by expressing the product of a skew Schur function and a single row Schur function in terms of skew Schur functions. Like the classical rule, our rule involves simple additions of boxes to the original skew shape. Our proof is purely combinatorial and extends the combinatorial proof of the classical case.
Assaf, Sami H. and McNamara, Peter R. W.. "A Pieri Rule for Skew Shapes." Journal of Combinatorial Theory (Series A) 118, no. 1 (2011) : 277-290.