Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001122
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Mapping
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St001122: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,0,0,1,0]
 => [[2,2],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,0]
 => [[2,2,1],[1]]
 => [1]
 => 1
[1,1,0,0,1,0,1,0]
 => [[2,2,2],[1,1]]
 => [1,1]
 => 0
[1,1,0,0,1,1,0,0]
 => [[3,2],[1]]
 => [1]
 => 1
[1,1,0,1,0,0,1,0]
 => [[3,3],[2]]
 => [2]
 => 0
[1,1,0,1,1,0,0,0]
 => [[3,3],[1]]
 => [1]
 => 1
[1,1,1,0,0,0,1,0]
 => [[2,2,2],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1],[1,1]]
 => [1,1]
 => 0
[1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1],[2]]
 => [2]
 => 0
[1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1],[1]]
 => [1]
 => 1
[1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1],[1]]
 => [1]
 => 1
[1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 0
[1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2],[1,1]]
 => [1,1]
 => 0
[1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => [2,1]
 => 1
[1,1,0,0,1,1,0,1,0,0]
 => [[4,2],[1]]
 => [1]
 => 1
[1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => 0
[1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3],[2,2]]
 => [2,2]
 => 1
[1,1,0,1,0,0,1,1,0,0]
 => [[4,3],[2]]
 => [2]
 => 0
[1,1,0,1,0,1,0,0,1,0]
 => [[4,4],[3]]
 => [3]
 => 0
[1,1,0,1,0,1,1,0,0,0]
 => [[4,4],[2]]
 => [2]
 => 0
[1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3],[2,1]]
 => [2,1]
 => 1
[1,1,0,1,1,0,0,1,0,0]
 => [[4,3],[1]]
 => [1]
 => 1
[1,1,0,1,1,0,1,0,0,0]
 => [[3,3,3],[1,1]]
 => [1,1]
 => 0
[1,1,0,1,1,1,0,0,0,0]
 => [[4,4],[1]]
 => [1]
 => 1
[1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2],[1,1]]
 => [1,1]
 => 0
[1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => [1]
 => 1
[1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2],[2]]
 => [2]
 => 0
[1,1,1,0,0,1,1,0,0,0]
 => [[3,3,2],[1]]
 => [1]
 => 1
[1,1,1,0,1,0,0,0,1,0]
 => [[2,2,2,2],[1]]
 => [1]
 => 1
[1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => 0
[1,1,1,1,0,0,1,0,0,0]
 => [[3,3,3],[1]]
 => [1]
 => 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1],[1,1]]
 => [1,1]
 => 0
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1,1],[2]]
 => [2]
 => 0
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => 0
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1],[1,1]]
 => [1,1]
 => 0
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1],[2,1]]
 => [2,1]
 => 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => [1,1]
 => 0
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1],[2,2]]
 => [2,2]
 => 1
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1],[2]]
 => [2]
 => 0
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [[4,4,1],[3]]
 => [3]
 => 0
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [[4,4,1],[2]]
 => [2]
 => 0
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => [2,1]
 => 1
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [[4,3,1],[1]]
 => [1]
 => 1
Description
The multiplicity of the sign 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 $g_{\lambda,\lambda}^{1^n}$, for $\lambda\vdash n$. It equals $1$ if and only if $\lambda$ is self-conjugate.