SP::TablePe --
table of the Pe-basis
Call(s)
SP::TablePe(n)
Parametersn | - | any positive integer denoting the degree of a symmetric group |
Introduction
The SP::TablePe function returns the table of all elements of the Pe-basis,
which is the dual basis of the basis of (increasing) monomials (less than
the ``staircase'' monomial), 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).
When called with the second argument X, it returns the table of
all polynomials in Sn, expressed in the Schubert basis.
Example 1>> t:=muEC::SP::TablePe(3);
table(
2
[2, 1, 0] = x1 x2,
2
[1, 1, 0] = x1 x2 + x1 ,
[1, 0, 0] = x1 + x2,
[2, 0, 0] = x1 x2,
[0, 1, 0] = x1,
[0, 0, 0] = 1
)
>> muEC::SP::TablePe(3, X);
table(
[2, 1, 0] = X[3, 2, 1],
[1, 1, 0] = X[2, 3, 1] + X[3, 1, 2],
[1, 0, 0] = X[1, 3, 2],
[2, 0, 0] = X[2, 3, 1],
[0, 1, 0] = X[2, 1],
[0, 0, 0] = X[1]
)
Related FunctionsMuPAD Combinat, an open source algebraic combinatorics package