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

#### Call(s)

`SP::TableYY(n)`

#### Parameters

`n` | - | any positive integer denoting the degree of a symmetric group
`perm` | - | any list denoting a permutation

#### Introduction

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]`.

#### Example 1

    >> 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
                   )

#### Related Functions

`TableY`

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MuPAD Combinat, an open source algebraic combinatorics package