muEC::SP::TableX – table of all Schubert polynomials

The muEC::SP::TableX function returns the table of all Schubert polynomials indexed by permutations in math. The polynomials are expressed in the basis of monomials.

When called with the second argument Pe, it returns the table of all Schubert polynomials in math, expressed in the dual basis of the monomial basis, i.e. the basis of products of elementary symmetric functions on an alphabet flag. For instance, Pe[1, 2, 0, 1, 0] stands for the product e1(x1,x2,x3,x4)*e2(x1,x2,x3)*e1(x1).

→ Examples

Call:

muEC::SP::TableX(n)

Parameters:

n

any positive integer denoting the degree of a symmetric group

Related Functions:

muEC::SP::TableXX

Example 1:

t:=muEC::SP::TableX(3);

math

t[ [2,3,1] ];

math

muEC::SP::TableX(3, Pe);

math