[Previous] [Next] [Contents]

## `SG::SgCharTable` -- computes the table of characters

#### Call(s)

`SG::SgCharTable(n <,part1> <,part2>)`
`SG::SgCharTable(n <,index>)`

#### Parameters

`n` | - | any positive integer denoting the degree of a symmetric group
`part1, part2` | - | any lists denoting partitions

#### Introduction

The `SG::SgCharTable` gives the table of characters for the symmetric group of order `n`. Let `t` be this matrix, `part1`, `part2` be two partitions of `n`, of index i, j in the list of partitions ``SG::SgCharTable`(n, index)`, then `t`[i,j] is equal to the value of the irreducible character of index `part1` on the conjugacy class indexed by `part2`.

#### Example 1

    >> muEC::SG::SgCharTable( 3 );

                                  +-           -+
                                  |   1,  1, 1  |
                                  |             |
                                  |  -1,  0, 2  |
                                  |             |
                                  |   1, -1, 1  |
                                  +-           -+

    >> muEC::SG::SgCharTable( 3, index );

                             [[3], [2, 1], [1, 1, 1]]

    >> muEC::SG::SgCharTable(3, [2,1], [1,1,1]);

                                         2

#### Related Functions

`TYP::IsPart`

[Previous] [Next] [Contents]

MuPAD Combinat, an open source algebraic combinatorics package