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## `SP::TableXX` -- table of all double Schubert polynomials

#### Call(s)

`SP::TableXX(n)`

#### Parameters

`n` | - | 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 Functions

`TableX`

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MuPAD Combinat, an open source algebraic combinatorics package