semistandardTableaux(Partition,ZZ) -- the list of semistandard tableaux of shape p and filling with the numbers from 0 to n-1.

Synopsis

Function: semistandardTableaux
Usage:

standardTableaux(p,n)
Inputs:
- p, an instance of the type Partition, the shape of the tableaux
- n, an integer, a limit of the range of numbers that appear in the tableaux
Outputs:
- an instance of the type TableauList, the list of semistandard tableaux

Description

The semistandard tableaux are tableaux that are strictly decreasing in rows and weakly decreasing in rows.

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

o1 = Partition{3, 2}

o1 : Partition

i2 : semistandardTableaux (p,4)

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

o2 : TableauList

Ways to use this method: