Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000202
Mapping
St000202: Cores ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([2],3)
 => 3
([1,1],3)
 => 3
([3,1],3)
 => 5
([2,1,1],3)
 => 5
([4,2],3)
 => 6
([3,1,1],3)
 => 7
([2,2,1,1],3)
 => 6
([5,3,1],3)
 => 9
([4,2,1,1],3)
 => 10
([3,2,2,1,1],3)
 => 9
([5,3,1,1],3)
 => 12
([4,2,2,1,1],3)
 => 12
([2],4)
 => 3
([1,1],4)
 => 3
([3],4)
 => 4
([2,1],4)
 => 5
([1,1,1],4)
 => 4
([4,1],4)
 => 7
([2,2],4)
 => 6
([3,1,1],4)
 => 8
([2,1,1,1],4)
 => 7
([5,2],4)
 => 9
([4,1,1],4)
 => 10
([3,2,1],4)
 => 10
([3,1,1,1],4)
 => 10
([2,2,1,1,1],4)
 => 9
([6,3],4)
 => 10
([5,2,1],4)
 => 14
([4,1,1,1],4)
 => 13
([4,2,2],4)
 => 13
([3,3,1,1],4)
 => 13
([3,2,1,1,1],4)
 => 14
([2,2,2,1,1,1],4)
 => 10
([2],5)
 => 3
([1,1],5)
 => 3
([3],5)
 => 4
([2,1],5)
 => 5
([1,1,1],5)
 => 4
([4],5)
 => 5
([3,1],5)
 => 7
([2,2],5)
 => 6
([2,1,1],5)
 => 7
([1,1,1,1],5)
 => 5
([5,1],5)
 => 9
([3,2],5)
 => 9
([4,1,1],5)
 => 11
([2,2,1],5)
 => 9
([3,1,1,1],5)
 => 11
([2,1,1,1,1],5)
 => 9
([6,2],5)
 => 12
Description
The number of k-cores contained in the k-core. Let $\lambda$ and $\mu$ be $k$-cores. Then $\lambda$ contains $\mu$ if and only if the Ferrers diagram of $\lambda$ contains the diagram of $\mu$. Each nonempty core trivially contains two other cores, the empty core and itself. The poset corresponding to containment is Young's lattice restricted to cores [1].