Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`Symmetry`
YoungTableauQ  |
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Details and Options
Examples
(10)
Scope
(5)
Valid tableaux
(1)
A staircase partition fills the rows in reading order and passes the validity test:
In[1]:=
YoungTableauQ[YoungTableau[{{1,2,3,4},{5,6,7},{8,9},{10}}]]
Out[2]=
True
The single-row partition is valid:
In[1]:=
YoungTableauQ[YoungTableau[{4}]]
Out[2]=
True
A two-cell hook:
In[1]:=
YoungTableauQ[YoungTableau[{2,1}]]
Out[2]=
True
Invalid forms
(1)
Bare list, not a YoungTableau
(1)
Non-standard entries
(1)
Validity caching
(1)
Applications
(2)
Properties & Relations
(3)
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Test whether an expression is a valid YoungTableau:
In[1]:=
YoungTableauQ[YoungTableau[{{1,2,3},{4,5}}]]
Out[1]=
True
The partition-form constructor also produces a valid tableau:
In[2]:=
YoungTableauQ[YoungTableau[{3,2}]]
Out[2]=
True
Row lengths that increase from top to bottom are not a valid partition shape:
In[3]:=
YoungTableauQ[YoungTableau[{{1,2},{3,4,5}}]]
Out[3]=
False
""