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TensorNetworks

Guides

  • TensorNetworks

Tech Notes

  • Building Tensor Networks
  • Contraction Paths and Execution
  • Matrix Product States
  • A Working Tour of the Symmetry Functions
  • Tensor Networks Overview
  • Young Tableaux and Tensor Symmetries

Symbols

  • ActivateTensors
  • BinaryTensorNetwork
  • BinaryTensorNetworkQ
  • CanonicalPath
  • CanonicalPathQ
  • ContractIndices
  • ContractionTree
  • EinsteinSummation
  • GreedyContractionPath
  • HookFactor
  • HookLength
  • HookLengths
  • IndexedMultiply
  • InitializeTensorNetwork
  • MetricTensor
  • MetricTensorQ
  • MPSCanonicalForm
  • MPSCanonicalQ
  • MPSEntanglementEntropy
  • MPSNormalize
  • MPSNorm
  • MPSOverlap
  • MPSSchmidtValues
  • MPSTruncate
  • OptimalContractionPath
  • PartitionQ
  • PathIndexContractions
  • PathQ
  • PathToTreePath
  • RandomTensorNetwork
  • SchurDimension
  • SparseTensorNetwork
  • TableauColumns
  • TableauDimension
  • TableauRows
  • TableauShape
  • TableauSize
  • TableauWeylDimension
  • TensorNetworkAdd
  • TensorNetworkContraction
  • TensorNetworkContractions
  • TensorNetworkContract
  • TensorNetworkData
  • TensorNetworkDelete
  • TensorNetworkFreeIndices
  • TensorNetworkGraphData
  • TensorNetworkGraphQ
  • TensorNetworkIndexDimensions
  • TensorNetworkIndexGraph
  • TensorNetworkIndices
  • TensorNetwork
  • TensorNetworkQ
  • TensorNetworkRemoveCycles
  • TensorNetworkReplaceIndices
  • TensorNetworkSize
  • TensorNetworkTensors
  • TensorNetworkToNetGraph
  • ToTensorNetworkGraph
  • TransposePartition
  • TreePathQ
  • TreePathToPath
  • YoungProject
  • YoungSymmetrize
  • YoungTableau
  • YoungTableauQ
Wolfram`TensorNetworks`Symmetry`
YoungTableau
​
YoungTableau
[rows]
represents a Young tableau, where
rows
is a list of lists of slot indices.
​
​
YoungTableau
[partition]
constructs a standard tableau from an integer
partition
, auto-filling rows in reading order.
​
Details and Options
Examples  
(11)
Scope  
(4)
From explicit rows  
(1)
The entries are slot labels; they need not be 1..n in reading order:
In[1]:=
YoungTableau
[{{2,4,5},{1,3}}]
Out[2]=
YoungTableau
Shape: {3,2}
Dimension: 5

​
The shape is determined by row lengths, not entry values:
In[1]:=
TableauShape

YoungTableau
[{{2,4,5},{1,3}}]
Out[2]=
{3,2}
From a partition  
(1)

Validity check  
(1)

Shape and size queries  
(1)

Applications  
(3)

Properties & Relations  
(4)

SeeAlso
YoungTableauQ
 
▪
TableauShape
 
▪
TableauSize
 
▪
TableauRows
 
▪
TableauColumns
 
▪
TableauDimension
 
▪
HookLengths
 
▪
YoungSymmetrize
 
▪
YoungProject
 
▪
PartitionQ
 
▪
Permutations
 
▪
IntegerPartitions
TechNotes
▪
Young Symmetries
RelatedGuides
▪
TensorNetworks
Construct a Young tableau from explicit rows:
In[1]:=
YoungTableau
[{{1,2,3},{4,5}}]
Out[1]=
YoungTableau
Shape: {3,2}
Dimension: 5

​
Construct a standard tableau from an integer partition; the rows are filled in reading order:
In[2]:=
YoungTableau
[{3,2}]
Out[2]=
YoungTableau
Shape: {3,2}
Dimension: 5

​
A larger staircase partition:
In[3]:=
YoungTableau
[{4,3,2,1}]
Out[3]=
YoungTableau
Shape: {4,3,2,1}
Dimension: 768

​
Read the shape and size of a tableau:
In[4]:=

TableauShape
[ytLocal$2225],
TableauSize
[ytLocal$2225]
Out[4]=
{{3,2},5}
""

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