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] => 1
([4,2],3) => [2,2] => 1
([3,1,1],3) => [2,1,1] => 1
([2,2,1,1],3) => [1,1,1,1] => 1
([5,3,1],3) => [2,2,1] => 1
([4,2,1,1],3) => [2,1,1,1] => 1
([3,2,2,1,1],3) => [1,1,1,1,1] => 1
([6,4,2],3) => [2,2,2] => 1
([5,3,1,1],3) => [2,2,1,1] => 1
([4,2,2,1,1],3) => [2,1,1,1,1] => 1
([3,3,2,2,1,1],3) => [1,1,1,1,1,1] => 1
([2],4) => [2] => 1
([1,1],4) => [1,1] => 1
([3],4) => [3] => 2
([2,1],4) => [2,1] => 1
([1,1,1],4) => [1,1,1] => 1
([4,1],4) => [3,1] => 2
([2,2],4) => [2,2] => 1
([3,1,1],4) => [2,1,1] => 1
([2,1,1,1],4) => [1,1,1,1] => 1
([5,2],4) => [3,2] => 2
([4,1,1],4) => [3,1,1] => 2
([3,2,1],4) => [2,2,1] => 1
([3,1,1,1],4) => [2,1,1,1] => 1
([2,2,1,1,1],4) => [1,1,1,1,1] => 1
([6,3],4) => [3,3] => 4
([5,2,1],4) => [3,2,1] => 2
([4,1,1,1],4) => [3,1,1,1] => 2
([4,2,2],4) => [2,2,2] => 1
([3,3,1,1],4) => [2,2,1,1] => 1
([3,2,1,1,1],4) => [2,1,1,1,1] => 1
([2,2,2,1,1,1],4) => [1,1,1,1,1,1] => 1
([2],5) => [2] => 1
([1,1],5) => [1,1] => 1
([3],5) => [3] => 2
([2,1],5) => [2,1] => 1
([1,1,1],5) => [1,1,1] => 1
([4],5) => [4] => 6
([3,1],5) => [3,1] => 2
([2,2],5) => [2,2] => 1
([2,1,1],5) => [2,1,1] => 1
([1,1,1,1],5) => [1,1,1,1] => 1
([5,1],5) => [4,1] => 6
([3,2],5) => [3,2] => 2
([4,1,1],5) => [3,1,1] => 2
([2,2,1],5) => [2,2,1] => 1
([3,1,1,1],5) => [2,1,1,1] => 1
([2,1,1,1,1],5) => [1,1,1,1,1] => 1
([6,2],5) => [4,2] => 6
([5,1,1],5) => [4,1,1] => 6
([3,3],5) => [3,3] => 4
([4,2,1],5) => [3,2,1] => 2
([4,1,1,1],5) => [3,1,1,1] => 2
([2,2,2],5) => [2,2,2] => 1
([3,2,1,1],5) => [2,2,1,1] => 1
([3,1,1,1,1],5) => [2,1,1,1,1] => 1
([2,2,1,1,1,1],5) => [1,1,1,1,1,1] => 1
([2],6) => [2] => 1
([1,1],6) => [1,1] => 1
([3],6) => [3] => 2
([2,1],6) => [2,1] => 1
([1,1,1],6) => [1,1,1] => 1
([4],6) => [4] => 6
([3,1],6) => [3,1] => 2
([2,2],6) => [2,2] => 1
([2,1,1],6) => [2,1,1] => 1
([1,1,1,1],6) => [1,1,1,1] => 1
([5],6) => [5] => 6
([4,1],6) => [4,1] => 6
([3,2],6) => [3,2] => 2
([3,1,1],6) => [3,1,1] => 2
([2,2,1],6) => [2,2,1] => 1
([2,1,1,1],6) => [2,1,1,1] => 1
([1,1,1,1,1],6) => [1,1,1,1,1] => 1
([6,1],6) => [5,1] => 6
([4,2],6) => [4,2] => 6
([5,1,1],6) => [4,1,1] => 6
([3,3],6) => [3,3] => 4
([3,2,1],6) => [3,2,1] => 2
([4,1,1,1],6) => [3,1,1,1] => 2
([2,2,2],6) => [2,2,2] => 1
([2,2,1,1],6) => [2,2,1,1] => 1
([3,1,1,1,1],6) => [2,1,1,1,1] => 1
([2,1,1,1,1,1],6) => [1,1,1,1,1,1] => 1
([7,2],6) => [5,2] => 6
([6,1,1],6) => [5,1,1] => 6
([4,3],6) => [4,3] => 12
([5,2,1],6) => [4,2,1] => 6
([5,1,1,1],6) => [4,1,1,1] => 6
([3,3,1],6) => [3,3,1] => 4
([3,2,2],6) => [3,2,2] => 2
([4,2,1,1],6) => [3,2,1,1] => 2
([4,1,1,1,1],6) => [3,1,1,1,1] => 2
([2,2,2,1],6) => [2,2,2,1] => 1
([3,2,1,1,1],6) => [2,2,1,1,1] => 1
([3,1,1,1,1,1],6) => [2,1,1,1,1,1] => 1
([2,2,1,1,1,1,1],6) => [1,1,1,1,1,1,1] => 1
search for individual values
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searching the database for statistics with the same generating function
Description
The number of conjugacy classes of subgroups with connected subgroups of sizes prescribed by an integer partition.
Equivalently, given an integer partition $\lambda$, this is the number of molecular combinatorial species that decompose into a product of atomic species of sizes $\lambda_1,\lambda_2,\dots$. In particular, the value on the partition $(n)$ is the number of atomic species of degree $n$, [2].
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].