Identifier
Values
([2],3) => [2] => 1
([1,1],3) => [1,1] => 1
([3,1],3) => [2,1] => 4
([2,1,1],3) => [1,1,1] => 1
([4,2],3) => [2,2] => 4
([3,1,1],3) => [2,1,1] => 11
([2,2,1,1],3) => [1,1,1,1] => 1
([5,3,1],3) => [2,2,1] => 34
([4,2,1,1],3) => [2,1,1,1] => 26
([3,2,2,1,1],3) => [1,1,1,1,1] => 1
([6,4,2],3) => [2,2,2] => 34
([5,3,1,1],3) => [2,2,1,1] => 180
([4,2,2,1,1],3) => [2,1,1,1,1] => 57
([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] => 1
([2,1],4) => [2,1] => 4
([1,1,1],4) => [1,1,1] => 1
([4,1],4) => [3,1] => 7
([2,2],4) => [2,2] => 4
([3,1,1],4) => [2,1,1] => 11
([2,1,1,1],4) => [1,1,1,1] => 1
([5,2],4) => [3,2] => 15
([4,1,1],4) => [3,1,1] => 32
([3,2,1],4) => [2,2,1] => 34
([3,1,1,1],4) => [2,1,1,1] => 26
([2,2,1,1,1],4) => [1,1,1,1,1] => 1
([6,3],4) => [3,3] => 15
([5,2,1],4) => [3,2,1] => 192
([4,1,1,1],4) => [3,1,1,1] => 122
([4,2,2],4) => [2,2,2] => 34
([3,3,1,1],4) => [2,2,1,1] => 180
([3,2,1,1,1],4) => [2,1,1,1,1] => 57
([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] => 1
([2,1],5) => [2,1] => 4
([1,1,1],5) => [1,1,1] => 1
([4],5) => [4] => 1
([3,1],5) => [3,1] => 7
([2,2],5) => [2,2] => 4
([2,1,1],5) => [2,1,1] => 11
([1,1,1,1],5) => [1,1,1,1] => 1
([5,1],5) => [4,1] => 11
([3,2],5) => [3,2] => 15
([4,1,1],5) => [3,1,1] => 32
([2,2,1],5) => [2,2,1] => 34
([3,1,1,1],5) => [2,1,1,1] => 26
([2,1,1,1,1],5) => [1,1,1,1,1] => 1
([6,2],5) => [4,2] => 26
([5,1,1],5) => [4,1,1] => 76
([3,3],5) => [3,3] => 15
([4,2,1],5) => [3,2,1] => 192
([4,1,1,1],5) => [3,1,1,1] => 122
([2,2,2],5) => [2,2,2] => 34
([3,2,1,1],5) => [2,2,1,1] => 180
([3,1,1,1,1],5) => [2,1,1,1,1] => 57
([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] => 1
([2,1],6) => [2,1] => 4
([1,1,1],6) => [1,1,1] => 1
([4],6) => [4] => 1
([3,1],6) => [3,1] => 7
([2,2],6) => [2,2] => 4
([2,1,1],6) => [2,1,1] => 11
([1,1,1,1],6) => [1,1,1,1] => 1
([5],6) => [5] => 1
([4,1],6) => [4,1] => 11
([3,2],6) => [3,2] => 15
([3,1,1],6) => [3,1,1] => 32
([2,2,1],6) => [2,2,1] => 34
([2,1,1,1],6) => [2,1,1,1] => 26
([1,1,1,1,1],6) => [1,1,1,1,1] => 1
([6,1],6) => [5,1] => 16
([4,2],6) => [4,2] => 26
([5,1,1],6) => [4,1,1] => 76
([3,3],6) => [3,3] => 15
([3,2,1],6) => [3,2,1] => 192
([4,1,1,1],6) => [3,1,1,1] => 122
([2,2,2],6) => [2,2,2] => 34
([2,2,1,1],6) => [2,2,1,1] => 180
([3,1,1,1,1],6) => [2,1,1,1,1] => 57
([2,1,1,1,1,1],6) => [1,1,1,1,1,1] => 1
([7,2],6) => [5,2] => 42
([6,1,1],6) => [5,1,1] => 156
([4,3],6) => [4,3] => 56
([5,2,1],6) => [4,2,1] => 474
([5,1,1,1],6) => [4,1,1,1] => 426
([3,3,1],6) => [3,3,1] => 267
([3,2,2],6) => [3,2,2] => 294
([4,2,1,1],6) => [3,2,1,1] => 1494
([4,1,1,1,1],6) => [3,1,1,1,1] => 423
([2,2,2,1],6) => [2,2,2,1] => 496
([3,2,1,1,1],6) => [2,2,1,1,1] => 768
([3,1,1,1,1,1],6) => [2,1,1,1,1,1] => 120
([2,2,1,1,1,1,1],6) => [1,1,1,1,1,1,1] => 1
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searching the database for statistics with the same generating function
Description
Number of permutations whose sorted list of non zero multiplicities of the Lehmer code is the given partition.
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].