Identifier
Values
([2],3) => [2] => 1
([1,1],3) => [1,1] => 1
([3,1],3) => [2,1] => 1
([2,1,1],3) => [1,1,1] => 0
([4,2],3) => [2,2] => 0
([3,1,1],3) => [2,1,1] => 1
([2,2,1,1],3) => [1,1,1,1] => 0
([5,3,1],3) => [2,2,1] => 1
([4,2,1,1],3) => [2,1,1,1] => 0
([3,2,2,1,1],3) => [1,1,1,1,1] => 0
([6,4,2],3) => [2,2,2] => 0
([5,3,1,1],3) => [2,2,1,1] => 0
([4,2,2,1,1],3) => [2,1,1,1,1] => 0
([3,3,2,2,1,1],3) => [1,1,1,1,1,1] => 0
([2],4) => [2] => 1
([1,1],4) => [1,1] => 1
([3],4) => [3] => 0
([2,1],4) => [2,1] => 1
([1,1,1],4) => [1,1,1] => 0
([4,1],4) => [3,1] => 1
([2,2],4) => [2,2] => 0
([3,1,1],4) => [2,1,1] => 1
([2,1,1,1],4) => [1,1,1,1] => 0
([5,2],4) => [3,2] => 1
([4,1,1],4) => [3,1,1] => 1
([3,2,1],4) => [2,2,1] => 1
([3,1,1,1],4) => [2,1,1,1] => 0
([2,2,1,1,1],4) => [1,1,1,1,1] => 0
([6,3],4) => [3,3] => 0
([5,2,1],4) => [3,2,1] => 2
([4,1,1,1],4) => [3,1,1,1] => 1
([4,2,2],4) => [2,2,2] => 0
([3,3,1,1],4) => [2,2,1,1] => 0
([3,2,1,1,1],4) => [2,1,1,1,1] => 0
([2,2,2,1,1,1],4) => [1,1,1,1,1,1] => 0
([2],5) => [2] => 1
([1,1],5) => [1,1] => 1
([3],5) => [3] => 0
([2,1],5) => [2,1] => 1
([1,1,1],5) => [1,1,1] => 0
([4],5) => [4] => 0
([3,1],5) => [3,1] => 1
([2,2],5) => [2,2] => 0
([2,1,1],5) => [2,1,1] => 1
([1,1,1,1],5) => [1,1,1,1] => 0
([5,1],5) => [4,1] => 0
([3,2],5) => [3,2] => 1
([4,1,1],5) => [3,1,1] => 1
([2,2,1],5) => [2,2,1] => 1
([3,1,1,1],5) => [2,1,1,1] => 0
([2,1,1,1,1],5) => [1,1,1,1,1] => 0
([6,2],5) => [4,2] => 0
([5,1,1],5) => [4,1,1] => 1
([3,3],5) => [3,3] => 0
([4,2,1],5) => [3,2,1] => 2
([4,1,1,1],5) => [3,1,1,1] => 1
([2,2,2],5) => [2,2,2] => 0
([3,2,1,1],5) => [2,2,1,1] => 0
([3,1,1,1,1],5) => [2,1,1,1,1] => 0
([2,2,1,1,1,1],5) => [1,1,1,1,1,1] => 0
([2],6) => [2] => 1
([1,1],6) => [1,1] => 1
([3],6) => [3] => 0
([2,1],6) => [2,1] => 1
([1,1,1],6) => [1,1,1] => 0
([4],6) => [4] => 0
([3,1],6) => [3,1] => 1
([2,2],6) => [2,2] => 0
([2,1,1],6) => [2,1,1] => 1
([1,1,1,1],6) => [1,1,1,1] => 0
([5],6) => [5] => 0
([4,1],6) => [4,1] => 0
([3,2],6) => [3,2] => 1
([3,1,1],6) => [3,1,1] => 1
([2,2,1],6) => [2,2,1] => 1
([2,1,1,1],6) => [2,1,1,1] => 0
([1,1,1,1,1],6) => [1,1,1,1,1] => 0
([6,1],6) => [5,1] => 0
([4,2],6) => [4,2] => 0
([5,1,1],6) => [4,1,1] => 1
([3,3],6) => [3,3] => 0
([3,2,1],6) => [3,2,1] => 2
([4,1,1,1],6) => [3,1,1,1] => 1
([2,2,2],6) => [2,2,2] => 0
([2,2,1,1],6) => [2,2,1,1] => 0
([3,1,1,1,1],6) => [2,1,1,1,1] => 0
([2,1,1,1,1,1],6) => [1,1,1,1,1,1] => 0
([7,2],6) => [5,2] => 0
([6,1,1],6) => [5,1,1] => 0
([4,3],6) => [4,3] => 0
([5,2,1],6) => [4,2,1] => 1
([5,1,1,1],6) => [4,1,1,1] => 1
([3,3,1],6) => [3,3,1] => 1
([3,2,2],6) => [3,2,2] => 1
([4,2,1,1],6) => [3,2,1,1] => 1
([4,1,1,1,1],6) => [3,1,1,1,1] => 0
([2,2,2,1],6) => [2,2,2,1] => 0
([3,2,1,1,1],6) => [2,2,1,1,1] => 0
([3,1,1,1,1,1],6) => [2,1,1,1,1,1] => 0
([2,2,1,1,1,1,1],6) => [1,1,1,1,1,1,1] => 0
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Description
The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a 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 $g_{\lambda,\lambda}^{21^{n-2}}$, for $\lambda\vdash n$.
Map
to bounded partition
Description
The (k-1)-bounded partition of a k-core.
Starting with a $k$-core, deleting all cells of hook length greater than or equal to $k$ yields a $(k-1)$-bounded partition [1, Theorem 7], see also [2, Section 1.2].