Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`Symmetry`
TableauShape  |
|
| | ||||
▪
▪
The returned list always satisfies (non-increasing positive integers); validity of the input is guaranteed by the check on the argument.
▪
▪
The conjugate (transpose) partition is given by , which records the column lengths of the Young diagram.
▪
The irrep dimension depends only on the shape, so two tableaux with the same always carry the same irreducible representation of the symmetric group.
▪
Examples
(15)
Basic Examples
(3)
Shape of a {3,2} tableau:
In[1]:=
 | TableauShape |
 | YoungTableau |
Out[1]=
{3,2}
The shape of a tableau built from a partition is that very partition:
In[1]:=
| TableauShape |
| YoungTableau |
Out[1]=
{4,3,2,1}
A single-row tableau has shape {n}:
In[1]:=
| TableauShape |
| YoungTableau |
Out[1]=
{4}
Scope
(4)
Applications
(2)
Properties & Relations
(6)
 |
|
 |
|
 |
|
""