Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000192
Mapping
St000192: Cores ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([2],3)
 => 1
([1,1],3)
 => 1
([3,1],3)
 => 2
([2,1,1],3)
 => 2
([4,2],3)
 => 1
([3,1,1],3)
 => 1
([2,2,1,1],3)
 => 1
([5,3,1],3)
 => 2
([4,2,1,1],3)
 => 2
([3,2,2,1,1],3)
 => 2
([6,4,2],3)
 => 1
([5,3,1,1],3)
 => 1
([4,2,2,1,1],3)
 => 1
([3,3,2,2,1,1],3)
 => 1
([2],4)
 => 2
([1,1],4)
 => 2
([3],4)
 => 1
([2,1],4)
 => 2
([1,1,1],4)
 => 1
([4,1],4)
 => 2
([2,2],4)
 => 1
([3,1,1],4)
 => 3
([2,1,1,1],4)
 => 2
([5,2],4)
 => 2
([4,1,1],4)
 => 2
([3,2,1],4)
 => 2
([3,1,1,1],4)
 => 2
([2,2,1,1,1],4)
 => 2
([6,3],4)
 => 1
([5,2,1],4)
 => 2
([4,1,1,1],4)
 => 1
([4,2,2],4)
 => 2
([3,3,1,1],4)
 => 2
([3,2,1,1,1],4)
 => 2
([2,2,2,1,1,1],4)
 => 1
([2],5)
 => 2
([1,1],5)
 => 2
([3],5)
 => 2
([2,1],5)
 => 3
([1,1,1],5)
 => 2
([4],5)
 => 1
([3,1],5)
 => 2
([2,2],5)
 => 2
([2,1,1],5)
 => 2
([1,1,1,1],5)
 => 1
([5,1],5)
 => 2
([3,2],5)
 => 2
([4,1,1],5)
 => 3
([2,2,1],5)
 => 2
([3,1,1,1],5)
 => 3
Description
Number of covers of a core in weak Bruhat order. For k-cores, $\lambda$ covers $\mu$ if there exists an affine Grassmannian element $s_i$ such that the left action $s_i \cdot \mu = \lambda$.