Schur polynomial [SEP] named after
Schur polynomial
In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in "n" variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters of polynomial irreducible representations of the general linear groups. The Schur polynomials form a linear basis for the space of all symmetric polynomials. Any product of Schur functions can be written as a linear combination of Schur polynomials with non-negative integral coefficients; the values of these coefficients
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 "s" indexed by partitions λ, it states that
where "h" 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.