SP::TableXX --
table of all double Schubert polynomials
Call(s)
SP::TableXX(n)
Parametersn | - | any positive integer denoting the degree of a symmetric group |
perm | - | any list denoting a permutation |
Introduction
The SP::TableXX function returns the table of all double Schubert polynomials
indexed by permutations in Sn. The polynomials are expressed
in the basis of monomials.
When the function is called with the second argument perm, the second alphabet (the yi's) is specialized as the permutation perm of the first one (the xi's): in other words, y.i is sent to x.perm[i].
Example 1>> t:=muEC::SP::TableXX(3);
table(
[3, 2, 1] = (x1 - y1) (x1 - y2) (x2 - y1),
[2, 3, 1] = (x1 - y1) (x2 - y1),
[2, 1, 3] = x1 - y1,
[3, 1, 2] = (x1 - y1) (x1 - y2),
[1, 3, 2] = x1 + x2 - y1 - y2,
[1, 2, 3] = 1
)
>> t[ [3,1,2] ];
(x1 - y1) (x1 - y2)
>> muEC::SP::TableXX(3, [3,2,1]);
table(
[3, 2, 1] = (x1 - x2) (x1 - x3) (x2 - x3),
[2, 3, 1] = (x1 - x3) (x2 - x3),
[2, 1, 3] = x1 - x3,
[3, 1, 2] = (x1 - x2) (x1 - x3),
[1, 3, 2] = x1 - x3,
[1, 2, 3] = 1
)
Related FunctionsMuPAD Combinat, an open source algebraic combinatorics package