Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001121
Mapping
St001121: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 1
[1,1]
 => 0
[3]
 => 1
[2,1]
 => 1
[1,1,1]
 => 0
[4]
 => 1
[3,1]
 => 1
[2,2]
 => 1
[2,1,1]
 => 1
[1,1,1,1]
 => 0
[5]
 => 1
[4,1]
 => 1
[3,2]
 => 1
[3,1,1]
 => 1
[2,2,1]
 => 1
[2,1,1,1]
 => 0
[1,1,1,1,1]
 => 0
[6]
 => 1
[5,1]
 => 1
[4,2]
 => 2
[4,1,1]
 => 1
[3,3]
 => 0
[3,2,1]
 => 5
[3,1,1,1]
 => 1
[2,2,2]
 => 1
[2,2,1,1]
 => 0
[2,1,1,1,1]
 => 0
[1,1,1,1,1,1]
 => 0
[7]
 => 1
[6,1]
 => 1
[5,2]
 => 2
[5,1,1]
 => 1
[4,3]
 => 1
[4,2,1]
 => 9
[4,1,1,1]
 => 1
[3,3,1]
 => 1
[3,2,2]
 => 2
[3,2,1,1]
 => 8
[3,1,1,1,1]
 => 1
[2,2,2,1]
 => 1
[2,2,1,1,1]
 => 0
[2,1,1,1,1,1]
 => 0
[1,1,1,1,1,1,1]
 => 0
[8]
 => 1
[7,1]
 => 1
[6,2]
 => 2
[6,1,1]
 => 1
[5,3]
 => 1
[5,2,1]
 => 9
Description
The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition. The Kronecker coefficient is the multiplicity $g_{\mu,\nu}^\lambda$ of the Specht module $S^\lambda$ in $S^\mu\otimes S^\nu$: $$ S^\mu\otimes S^\nu = \bigoplus_\lambda g_{\mu,\nu}^\lambda S^\lambda $$ This statistic records the Kronecker coefficient $g_{\lambda,\lambda}^\lambda$.