tabloids(Partition) -- the list of tabloids for a given partition

Synopsis

Function: tabloids
Usage:

tabloids(p)
Inputs:
- p, an instance of the type Partition,
Outputs:
- an instance of the type TableauList, the list of tabloids

Description

Tabloids are the equivalence class of tableaux under the row permutation equivalence relation. Two tabloids are row permutation equivalent if one can be obtained from the other by permuting elements in its rows. For every tabloid there is a unique representative such that its rows are increasing. This representatives are the ones calculated by the method tabloids().

Tabloids are the basis of the permutation modules from which the Specht Modules are constructed.

i1 : p = new Partition from {3,2}

o1 = Partition{3, 2}

o1 : Partition

i2 : tabloids p

o2 = {| 0 1 2 |, | 0 1 3 |, | 0 1 4 |, | 0 2 3 |, | 0 2 4 |, | 0 3 4 |, | 1 2 3 |, | 1 2 4 |, | 1 3 4 |, | 2 3 4 |}
      | 3 4 |    | 2 4 |    | 2 3 |    | 1 4 |    | 1 3 |    | 1 2 |    | 0 4 |    | 0 3 |    | 0 2 |    | 0 1 |

o2 : TableauList

Ways to use this method: