SP::TableX
--
table of all Schubert polynomials
SP::TableX(n)
n | - | any positive integer denoting the degree of a symmetric group |
The SP::TableX
function returns the table of all Schubert polynomials
indexed by permutations in Sn.
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 Sn, 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)
.
>> t:=muEC::SP::TableX(3);
table( 2 [3, 2, 1] = x1 x2, [2, 3, 1] = x1 x2, [2, 1, 3] = x1, 2 [3, 1, 2] = x1 , [1, 3, 2] = x1 + x2, [1, 2, 3] = 1 )
>> t[ [2,3,1] ];
x1 x2
>> muEC::SP::TableX(3, Pe);
table( [3, 2, 1] = Pe[2, 1, 0], [2, 3, 1] = Pe[2, 0, 0], [2, 1, 3] = Pe[1, 0], [3, 1, 2] = Pe[1, 1, 0] - Pe[2, 0, 0], [1, 3, 2] = Pe[1, 0, 0], [1, 2, 3] = Pe[0] )
MuPAD Combinat, an open source algebraic combinatorics package