This method computes the standard scalar product on the ring Λ of symmetric functions. One way to define this product is by imposing that the collection of Schur functions sλ form an orthonormal basis.
Alternatively, by the correspondence between symmetric functions and virtual characters of symmetric groups, this scalar product coincides with the standard scalar product on class functions.
The number of standard tableaux of shape {4,3,2,1} is:
i1 : R = symmetricRing(QQ,10); |
i2 : S = schurRing(QQ,s,10); |
i3 : scalarProduct(h_1^10,s_{4,3,2,1}) o3 = 768 o3 : QQ |