standardTableaux(Partition) -- the list of standard tableaux of shape p

Synopsis

Function: standardTableaux
Usage:

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

Description

The standard tableaux of a given partition $\lambda$ are tableaux of shape p. Such that they are both row and column increasing. This set of tableaux are very important because they are in bijection with the basis of the Specht module $S^\lambda$.

The method calculates this tableaux recursively filling the cells of the Ferrer diagram and checking if the rows and columns are still increasing.

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

o1 = Partition{3, 2}

o1 : Partition

i2 : standardTableaux p

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

o2 : TableauList