Pieri's formula
In mathematics, Pieri's formula, named after Mario Pieri, describes the product of a Schubert cycle by a special Schubert cycle in the Schubert calculus, or the product of a Schur polynomial by a complete symmetric function. In terms of Schur functions sλ indexed by partitions λ, it states that s μ h r = ∑ λ s λ {\displaystyle \displaystyle s_{\mu }h_{r}=\sum _{\lambda }s_{\lambda }} where hr is a complete homogeneous symmetric polynomial and the sum is over all partitions λ obtained from μ by adding r elements, no two in the same column.