# 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 decreasign in rows and weakly deacreasing 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