SP::TableYY
--
table of all double Schubert polynomials
SP::TableYY(n)
n | - | any positive integer denoting the degree of a symmetric group |
perm | - | any list denoting a permutation |
The SP::TableYY
function returns the table of all double Schubert
polynomials indexed by codes of permutations in Sn.
The polynomials are expressed in the basis of monomials.
When called with the second argument perm, the second alphabet (the y
i'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]
.
>> t:=muEC::SP::TableYY(3);
table( [2, 1, 0] = (x1 - y1) (x1 - y2) (x2 - y1), [1, 1, 0] = (x1 - y1) (x2 - y1), [1, 0, 0] = x1 - y1, [2, 0, 0] = (x1 - y1) (x1 - y2), [0, 1, 0] = x1 + x2 - y1 - y2, [0, 0, 0] = 1 )
>> t[ [0,1,0] ];
x1 + x2 - y1 - y2
>> muEC::SP::TableYY(3, [3,2,1]);
table( [2, 1, 0] = (x1 - x2) (x1 - x3) (x2 - x3), [1, 1, 0] = (x1 - x3) (x2 - x3), [1, 0, 0] = x1 - x3, [2, 0, 0] = (x1 - x2) (x1 - x3), [0, 1, 0] = x1 - x3, [0, 0, 0] = 1 )
MuPAD Combinat, an open source algebraic combinatorics package