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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000897
St000897: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 1
[2]
=> 1
[1,1]
=> 1
[3]
=> 1
[2,1]
=> 1
[1,1,1]
=> 1
[4]
=> 1
[3,1]
=> 1
[2,2]
=> 1
[2,1,1]
=> 2
[1,1,1,1]
=> 1
[5]
=> 1
[4,1]
=> 1
[3,2]
=> 1
[3,1,1]
=> 2
[2,2,1]
=> 2
[2,1,1,1]
=> 2
[1,1,1,1,1]
=> 1
[6]
=> 1
[5,1]
=> 1
[4,2]
=> 1
[4,1,1]
=> 2
[3,3]
=> 1
[3,2,1]
=> 1
[3,1,1,1]
=> 2
[2,2,2]
=> 1
[2,2,1,1]
=> 1
[2,1,1,1,1]
=> 2
[1,1,1,1,1,1]
=> 1
[7]
=> 1
[6,1]
=> 1
[5,2]
=> 1
[5,1,1]
=> 2
[4,3]
=> 1
[4,2,1]
=> 1
[4,1,1,1]
=> 2
[3,3,1]
=> 2
[3,2,2]
=> 2
[3,2,1,1]
=> 2
[3,1,1,1,1]
=> 2
[2,2,2,1]
=> 2
[2,2,1,1,1]
=> 2
[2,1,1,1,1,1]
=> 2
[1,1,1,1,1,1,1]
=> 1
[8]
=> 1
[7,1]
=> 1
[6,2]
=> 1
[6,1,1]
=> 2
[5,3]
=> 1
[5,2,1]
=> 1
Description
The number of different multiplicities of parts of an integer partition.
Matching statistic: St000903
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St000903: Integer compositions ⟶ ℤResult quality: 57% ●values known / values provided: 57%●distinct values known / distinct values provided: 75%
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St000903: Integer compositions ⟶ ℤResult quality: 57% ●values known / values provided: 57%●distinct values known / distinct values provided: 75%
Values
[1]
=> [[1]]
=> [1] => [1] => 1
[2]
=> [[1,2]]
=> [2] => [1] => 1
[1,1]
=> [[1],[2]]
=> [1,1] => [2] => 1
[3]
=> [[1,2,3]]
=> [3] => [1] => 1
[2,1]
=> [[1,2],[3]]
=> [2,1] => [1,1] => 1
[1,1,1]
=> [[1],[2],[3]]
=> [1,1,1] => [3] => 1
[4]
=> [[1,2,3,4]]
=> [4] => [1] => 1
[3,1]
=> [[1,2,3],[4]]
=> [3,1] => [1,1] => 1
[2,2]
=> [[1,2],[3,4]]
=> [2,2] => [2] => 1
[2,1,1]
=> [[1,2],[3],[4]]
=> [2,1,1] => [1,2] => 2
[1,1,1,1]
=> [[1],[2],[3],[4]]
=> [1,1,1,1] => [4] => 1
[5]
=> [[1,2,3,4,5]]
=> [5] => [1] => 1
[4,1]
=> [[1,2,3,4],[5]]
=> [4,1] => [1,1] => 1
[3,2]
=> [[1,2,3],[4,5]]
=> [3,2] => [1,1] => 1
[3,1,1]
=> [[1,2,3],[4],[5]]
=> [3,1,1] => [1,2] => 2
[2,2,1]
=> [[1,2],[3,4],[5]]
=> [2,2,1] => [2,1] => 2
[2,1,1,1]
=> [[1,2],[3],[4],[5]]
=> [2,1,1,1] => [1,3] => 2
[1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [1,1,1,1,1] => [5] => 1
[6]
=> [[1,2,3,4,5,6]]
=> [6] => [1] => 1
[5,1]
=> [[1,2,3,4,5],[6]]
=> [5,1] => [1,1] => 1
[4,2]
=> [[1,2,3,4],[5,6]]
=> [4,2] => [1,1] => 1
[4,1,1]
=> [[1,2,3,4],[5],[6]]
=> [4,1,1] => [1,2] => 2
[3,3]
=> [[1,2,3],[4,5,6]]
=> [3,3] => [2] => 1
[3,2,1]
=> [[1,2,3],[4,5],[6]]
=> [3,2,1] => [1,1,1] => 1
[3,1,1,1]
=> [[1,2,3],[4],[5],[6]]
=> [3,1,1,1] => [1,3] => 2
[2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [2,2,2] => [3] => 1
[2,2,1,1]
=> [[1,2],[3,4],[5],[6]]
=> [2,2,1,1] => [2,2] => 1
[2,1,1,1,1]
=> [[1,2],[3],[4],[5],[6]]
=> [2,1,1,1,1] => [1,4] => 2
[1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6]]
=> [1,1,1,1,1,1] => [6] => 1
[7]
=> [[1,2,3,4,5,6,7]]
=> [7] => [1] => 1
[6,1]
=> [[1,2,3,4,5,6],[7]]
=> [6,1] => [1,1] => 1
[5,2]
=> [[1,2,3,4,5],[6,7]]
=> [5,2] => [1,1] => 1
[5,1,1]
=> [[1,2,3,4,5],[6],[7]]
=> [5,1,1] => [1,2] => 2
[4,3]
=> [[1,2,3,4],[5,6,7]]
=> [4,3] => [1,1] => 1
[4,2,1]
=> [[1,2,3,4],[5,6],[7]]
=> [4,2,1] => [1,1,1] => 1
[4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [4,1,1,1] => [1,3] => 2
[3,3,1]
=> [[1,2,3],[4,5,6],[7]]
=> [3,3,1] => [2,1] => 2
[3,2,2]
=> [[1,2,3],[4,5],[6,7]]
=> [3,2,2] => [1,2] => 2
[3,2,1,1]
=> [[1,2,3],[4,5],[6],[7]]
=> [3,2,1,1] => [1,1,2] => 2
[3,1,1,1,1]
=> [[1,2,3],[4],[5],[6],[7]]
=> [3,1,1,1,1] => [1,4] => 2
[2,2,2,1]
=> [[1,2],[3,4],[5,6],[7]]
=> [2,2,2,1] => [3,1] => 2
[2,2,1,1,1]
=> [[1,2],[3,4],[5],[6],[7]]
=> [2,2,1,1,1] => [2,3] => 2
[2,1,1,1,1,1]
=> [[1,2],[3],[4],[5],[6],[7]]
=> [2,1,1,1,1,1] => [1,5] => 2
[1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7]]
=> [1,1,1,1,1,1,1] => [7] => 1
[8]
=> [[1,2,3,4,5,6,7,8]]
=> [8] => [1] => 1
[7,1]
=> [[1,2,3,4,5,6,7],[8]]
=> [7,1] => [1,1] => 1
[6,2]
=> [[1,2,3,4,5,6],[7,8]]
=> [6,2] => [1,1] => 1
[6,1,1]
=> [[1,2,3,4,5,6],[7],[8]]
=> [6,1,1] => [1,2] => 2
[5,3]
=> [[1,2,3,4,5],[6,7,8]]
=> [5,3] => [1,1] => 1
[5,2,1]
=> [[1,2,3,4,5],[6,7],[8]]
=> [5,2,1] => [1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
=> [1,1,1,1,1,1,1,1,1,1] => [10] => ? = 1
[11]
=> [[1,2,3,4,5,6,7,8,9,10,11]]
=> ? => ? => ? = 1
[10,1]
=> [[1,2,3,4,5,6,7,8,9,10],[11]]
=> ? => ? => ? = 1
[9,2]
=> [[1,2,3,4,5,6,7,8,9],[10,11]]
=> ? => ? => ? = 1
[9,1,1]
=> [[1,2,3,4,5,6,7,8,9],[10],[11]]
=> ? => ? => ? = 2
[8,3]
=> [[1,2,3,4,5,6,7,8],[9,10,11]]
=> ? => ? => ? = 1
[8,2,1]
=> [[1,2,3,4,5,6,7,8],[9,10],[11]]
=> ? => ? => ? = 1
[8,1,1,1]
=> [[1,2,3,4,5,6,7,8],[9],[10],[11]]
=> ? => ? => ? = 2
[7,4]
=> [[1,2,3,4,5,6,7],[8,9,10,11]]
=> ? => ? => ? = 1
[7,3,1]
=> [[1,2,3,4,5,6,7],[8,9,10],[11]]
=> ? => ? => ? = 1
[7,2,2]
=> [[1,2,3,4,5,6,7],[8,9],[10,11]]
=> ? => ? => ? = 2
[7,2,1,1]
=> [[1,2,3,4,5,6,7],[8,9],[10],[11]]
=> ? => ? => ? = 2
[7,1,1,1,1]
=> [[1,2,3,4,5,6,7],[8],[9],[10],[11]]
=> ? => ? => ? = 2
[6,5]
=> [[1,2,3,4,5,6],[7,8,9,10,11]]
=> ? => ? => ? = 1
[6,4,1]
=> [[1,2,3,4,5,6],[7,8,9,10],[11]]
=> ? => ? => ? = 1
[6,3,2]
=> [[1,2,3,4,5,6],[7,8,9],[10,11]]
=> ? => ? => ? = 1
[6,3,1,1]
=> [[1,2,3,4,5,6],[7,8,9],[10],[11]]
=> ? => ? => ? = 2
[6,2,2,1]
=> [[1,2,3,4,5,6],[7,8],[9,10],[11]]
=> ? => ? => ? = 2
[6,2,1,1,1]
=> [[1,2,3,4,5,6],[7,8],[9],[10],[11]]
=> ? => ? => ? = 2
[6,1,1,1,1,1]
=> [[1,2,3,4,5,6],[7],[8],[9],[10],[11]]
=> ? => ? => ? = 2
[5,5,1]
=> [[1,2,3,4,5],[6,7,8,9,10],[11]]
=> ? => ? => ? = 2
[5,4,2]
=> [[1,2,3,4,5],[6,7,8,9],[10,11]]
=> [5,4,2] => ? => ? = 1
[5,4,1,1]
=> [[1,2,3,4,5],[6,7,8,9],[10],[11]]
=> [5,4,1,1] => ? => ? = 2
[5,3,3]
=> [[1,2,3,4,5],[6,7,8],[9,10,11]]
=> [5,3,3] => ? => ? = 2
[5,3,2,1]
=> [[1,2,3,4,5],[6,7,8],[9,10],[11]]
=> [5,3,2,1] => ? => ? = 1
[5,3,1,1,1]
=> [[1,2,3,4,5],[6,7,8],[9],[10],[11]]
=> [5,3,1,1,1] => ? => ? = 2
[5,2,2,2]
=> [[1,2,3,4,5],[6,7],[8,9],[10,11]]
=> [5,2,2,2] => ? => ? = 2
[5,2,2,1,1]
=> [[1,2,3,4,5],[6,7],[8,9],[10],[11]]
=> [5,2,2,1,1] => ? => ? = 2
[5,2,1,1,1,1]
=> [[1,2,3,4,5],[6,7],[8],[9],[10],[11]]
=> ? => ? => ? = 2
[5,1,1,1,1,1,1]
=> [[1,2,3,4,5],[6],[7],[8],[9],[10],[11]]
=> ? => ? => ? = 2
[4,4,2,1]
=> [[1,2,3,4],[5,6,7,8],[9,10],[11]]
=> [4,4,2,1] => ? => ? = 2
[4,4,1,1,1]
=> [[1,2,3,4],[5,6,7,8],[9],[10],[11]]
=> [4,4,1,1,1] => ? => ? = 2
[4,3,3,1]
=> [[1,2,3,4],[5,6,7],[8,9,10],[11]]
=> [4,3,3,1] => ? => ? = 2
[4,3,2,2]
=> [[1,2,3,4],[5,6,7],[8,9],[10,11]]
=> [4,3,2,2] => ? => ? = 2
[4,3,2,1,1]
=> [[1,2,3,4],[5,6,7],[8,9],[10],[11]]
=> [4,3,2,1,1] => ? => ? = 2
[4,3,1,1,1,1]
=> [[1,2,3,4],[5,6,7],[8],[9],[10],[11]]
=> ? => ? => ? = 2
[4,2,2,2,1]
=> [[1,2,3,4],[5,6],[7,8],[9,10],[11]]
=> [4,2,2,2,1] => ? => ? = 2
[4,2,2,1,1,1]
=> [[1,2,3,4],[5,6],[7,8],[9],[10],[11]]
=> ? => ? => ? = 3
[4,2,1,1,1,1,1]
=> [[1,2,3,4],[5,6],[7],[8],[9],[10],[11]]
=> ? => ? => ? = 2
[4,1,1,1,1,1,1,1]
=> [[1,2,3,4],[5],[6],[7],[8],[9],[10],[11]]
=> ? => ? => ? = 2
[3,3,3,1,1]
=> [[1,2,3],[4,5,6],[7,8,9],[10],[11]]
=> [3,3,3,1,1] => ? => ? = 2
[3,3,2,2,1]
=> [[1,2,3],[4,5,6],[7,8],[9,10],[11]]
=> [3,3,2,2,1] => ? => ? = 2
[3,3,2,1,1,1]
=> [[1,2,3],[4,5,6],[7,8],[9],[10],[11]]
=> ? => ? => ? = 3
[3,3,1,1,1,1,1]
=> [[1,2,3],[4,5,6],[7],[8],[9],[10],[11]]
=> ? => ? => ? = 2
[3,2,2,2,2]
=> [[1,2,3],[4,5],[6,7],[8,9],[10,11]]
=> ? => ? => ? = 2
[3,2,2,2,1,1]
=> [[1,2,3],[4,5],[6,7],[8,9],[10],[11]]
=> ? => ? => ? = 3
[3,2,2,1,1,1,1]
=> [[1,2,3],[4,5],[6,7],[8],[9],[10],[11]]
=> ? => ? => ? = 3
[3,2,1,1,1,1,1,1]
=> [[1,2,3],[4,5],[6],[7],[8],[9],[10],[11]]
=> ? => ? => ? = 2
[3,1,1,1,1,1,1,1,1]
=> [[1,2,3],[4],[5],[6],[7],[8],[9],[10],[11]]
=> ? => ? => ? = 2
[2,2,2,2,2,1]
=> [[1,2],[3,4],[5,6],[7,8],[9,10],[11]]
=> ? => ? => ? = 2
Description
The number of different parts of an integer composition.
Matching statistic: St000905
(load all 9 compositions to match this statistic)
(load all 9 compositions to match this statistic)
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
St000905: Integer compositions ⟶ ℤResult quality: 35% ●values known / values provided: 35%●distinct values known / distinct values provided: 50%
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
St000905: Integer compositions ⟶ ℤResult quality: 35% ●values known / values provided: 35%●distinct values known / distinct values provided: 50%
Values
[1]
=> [[1]]
=> [1] => 1
[2]
=> [[1,2]]
=> [2] => 1
[1,1]
=> [[1],[2]]
=> [1,1] => 1
[3]
=> [[1,2,3]]
=> [3] => 1
[2,1]
=> [[1,2],[3]]
=> [2,1] => 1
[1,1,1]
=> [[1],[2],[3]]
=> [1,1,1] => 1
[4]
=> [[1,2,3,4]]
=> [4] => 1
[3,1]
=> [[1,2,3],[4]]
=> [3,1] => 1
[2,2]
=> [[1,2],[3,4]]
=> [2,2] => 1
[2,1,1]
=> [[1,2],[3],[4]]
=> [2,1,1] => 2
[1,1,1,1]
=> [[1],[2],[3],[4]]
=> [1,1,1,1] => 1
[5]
=> [[1,2,3,4,5]]
=> [5] => 1
[4,1]
=> [[1,2,3,4],[5]]
=> [4,1] => 1
[3,2]
=> [[1,2,3],[4,5]]
=> [3,2] => 1
[3,1,1]
=> [[1,2,3],[4],[5]]
=> [3,1,1] => 2
[2,2,1]
=> [[1,2],[3,4],[5]]
=> [2,2,1] => 2
[2,1,1,1]
=> [[1,2],[3],[4],[5]]
=> [2,1,1,1] => 2
[1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [1,1,1,1,1] => 1
[6]
=> [[1,2,3,4,5,6]]
=> [6] => 1
[5,1]
=> [[1,2,3,4,5],[6]]
=> [5,1] => 1
[4,2]
=> [[1,2,3,4],[5,6]]
=> [4,2] => 1
[4,1,1]
=> [[1,2,3,4],[5],[6]]
=> [4,1,1] => 2
[3,3]
=> [[1,2,3],[4,5,6]]
=> [3,3] => 1
[3,2,1]
=> [[1,2,3],[4,5],[6]]
=> [3,2,1] => 1
[3,1,1,1]
=> [[1,2,3],[4],[5],[6]]
=> [3,1,1,1] => 2
[2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [2,2,2] => 1
[2,2,1,1]
=> [[1,2],[3,4],[5],[6]]
=> [2,2,1,1] => 1
[2,1,1,1,1]
=> [[1,2],[3],[4],[5],[6]]
=> [2,1,1,1,1] => 2
[1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6]]
=> [1,1,1,1,1,1] => 1
[7]
=> [[1,2,3,4,5,6,7]]
=> [7] => 1
[6,1]
=> [[1,2,3,4,5,6],[7]]
=> [6,1] => 1
[5,2]
=> [[1,2,3,4,5],[6,7]]
=> [5,2] => 1
[5,1,1]
=> [[1,2,3,4,5],[6],[7]]
=> [5,1,1] => 2
[4,3]
=> [[1,2,3,4],[5,6,7]]
=> [4,3] => 1
[4,2,1]
=> [[1,2,3,4],[5,6],[7]]
=> [4,2,1] => 1
[4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [4,1,1,1] => 2
[3,3,1]
=> [[1,2,3],[4,5,6],[7]]
=> [3,3,1] => 2
[3,2,2]
=> [[1,2,3],[4,5],[6,7]]
=> [3,2,2] => 2
[3,2,1,1]
=> [[1,2,3],[4,5],[6],[7]]
=> [3,2,1,1] => 2
[3,1,1,1,1]
=> [[1,2,3],[4],[5],[6],[7]]
=> [3,1,1,1,1] => 2
[2,2,2,1]
=> [[1,2],[3,4],[5,6],[7]]
=> [2,2,2,1] => 2
[2,2,1,1,1]
=> [[1,2],[3,4],[5],[6],[7]]
=> [2,2,1,1,1] => 2
[2,1,1,1,1,1]
=> [[1,2],[3],[4],[5],[6],[7]]
=> [2,1,1,1,1,1] => 2
[1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7]]
=> [1,1,1,1,1,1,1] => 1
[8]
=> [[1,2,3,4,5,6,7,8]]
=> [8] => 1
[7,1]
=> [[1,2,3,4,5,6,7],[8]]
=> [7,1] => 1
[6,2]
=> [[1,2,3,4,5,6],[7,8]]
=> [6,2] => 1
[6,1,1]
=> [[1,2,3,4,5,6],[7],[8]]
=> [6,1,1] => 2
[5,3]
=> [[1,2,3,4,5],[6,7,8]]
=> [5,3] => 1
[5,2,1]
=> [[1,2,3,4,5],[6,7],[8]]
=> [5,2,1] => 1
[10]
=> [[1,2,3,4,5,6,7,8,9,10]]
=> [10] => ? = 1
[9,1]
=> [[1,2,3,4,5,6,7,8,9],[10]]
=> [9,1] => ? = 1
[8,2]
=> [[1,2,3,4,5,6,7,8],[9,10]]
=> [8,2] => ? = 1
[8,1,1]
=> [[1,2,3,4,5,6,7,8],[9],[10]]
=> [8,1,1] => ? = 2
[7,3]
=> [[1,2,3,4,5,6,7],[8,9,10]]
=> [7,3] => ? = 1
[7,2,1]
=> [[1,2,3,4,5,6,7],[8,9],[10]]
=> [7,2,1] => ? = 1
[7,1,1,1]
=> [[1,2,3,4,5,6,7],[8],[9],[10]]
=> [7,1,1,1] => ? = 2
[6,4]
=> [[1,2,3,4,5,6],[7,8,9,10]]
=> [6,4] => ? = 1
[6,3,1]
=> [[1,2,3,4,5,6],[7,8,9],[10]]
=> [6,3,1] => ? = 1
[6,2,2]
=> [[1,2,3,4,5,6],[7,8],[9,10]]
=> [6,2,2] => ? = 2
[6,2,1,1]
=> [[1,2,3,4,5,6],[7,8],[9],[10]]
=> [6,2,1,1] => ? = 2
[6,1,1,1,1]
=> [[1,2,3,4,5,6],[7],[8],[9],[10]]
=> [6,1,1,1,1] => ? = 2
[5,5]
=> [[1,2,3,4,5],[6,7,8,9,10]]
=> [5,5] => ? = 1
[5,4,1]
=> [[1,2,3,4,5],[6,7,8,9],[10]]
=> [5,4,1] => ? = 1
[5,3,2]
=> [[1,2,3,4,5],[6,7,8],[9,10]]
=> [5,3,2] => ? = 1
[5,3,1,1]
=> [[1,2,3,4,5],[6,7,8],[9],[10]]
=> [5,3,1,1] => ? = 2
[5,2,2,1]
=> [[1,2,3,4,5],[6,7],[8,9],[10]]
=> [5,2,2,1] => ? = 2
[5,2,1,1,1]
=> [[1,2,3,4,5],[6,7],[8],[9],[10]]
=> [5,2,1,1,1] => ? = 2
[5,1,1,1,1,1]
=> [[1,2,3,4,5],[6],[7],[8],[9],[10]]
=> [5,1,1,1,1,1] => ? = 2
[4,4,2]
=> [[1,2,3,4],[5,6,7,8],[9,10]]
=> [4,4,2] => ? = 2
[4,4,1,1]
=> [[1,2,3,4],[5,6,7,8],[9],[10]]
=> [4,4,1,1] => ? = 1
[4,3,3]
=> [[1,2,3,4],[5,6,7],[8,9,10]]
=> [4,3,3] => ? = 2
[4,3,2,1]
=> [[1,2,3,4],[5,6,7],[8,9],[10]]
=> [4,3,2,1] => ? = 1
[4,3,1,1,1]
=> [[1,2,3,4],[5,6,7],[8],[9],[10]]
=> [4,3,1,1,1] => ? = 2
[4,2,2,2]
=> [[1,2,3,4],[5,6],[7,8],[9,10]]
=> [4,2,2,2] => ? = 2
[4,2,2,1,1]
=> [[1,2,3,4],[5,6],[7,8],[9],[10]]
=> [4,2,2,1,1] => ? = 2
[4,2,1,1,1,1]
=> [[1,2,3,4],[5,6],[7],[8],[9],[10]]
=> [4,2,1,1,1,1] => ? = 2
[4,1,1,1,1,1,1]
=> [[1,2,3,4],[5],[6],[7],[8],[9],[10]]
=> [4,1,1,1,1,1,1] => ? = 2
[3,3,3,1]
=> [[1,2,3],[4,5,6],[7,8,9],[10]]
=> [3,3,3,1] => ? = 2
[3,3,2,2]
=> [[1,2,3],[4,5,6],[7,8],[9,10]]
=> [3,3,2,2] => ? = 1
[3,3,2,1,1]
=> [[1,2,3],[4,5,6],[7,8],[9],[10]]
=> [3,3,2,1,1] => ? = 2
[3,3,1,1,1,1]
=> [[1,2,3],[4,5,6],[7],[8],[9],[10]]
=> [3,3,1,1,1,1] => ? = 2
[3,2,2,2,1]
=> [[1,2,3],[4,5],[6,7],[8,9],[10]]
=> [3,2,2,2,1] => ? = 2
[3,2,2,1,1,1]
=> [[1,2,3],[4,5],[6,7],[8],[9],[10]]
=> [3,2,2,1,1,1] => ? = 3
[3,2,1,1,1,1,1]
=> [[1,2,3],[4,5],[6],[7],[8],[9],[10]]
=> [3,2,1,1,1,1,1] => ? = 2
[3,1,1,1,1,1,1,1]
=> [[1,2,3],[4],[5],[6],[7],[8],[9],[10]]
=> [3,1,1,1,1,1,1,1] => ? = 2
[2,2,2,2,2]
=> [[1,2],[3,4],[5,6],[7,8],[9,10]]
=> [2,2,2,2,2] => ? = 1
[2,2,2,2,1,1]
=> [[1,2],[3,4],[5,6],[7,8],[9],[10]]
=> [2,2,2,2,1,1] => ? = 2
[2,2,2,1,1,1,1]
=> [[1,2],[3,4],[5,6],[7],[8],[9],[10]]
=> [2,2,2,1,1,1,1] => ? = 2
[2,2,1,1,1,1,1,1]
=> [[1,2],[3,4],[5],[6],[7],[8],[9],[10]]
=> [2,2,1,1,1,1,1,1] => ? = 2
[2,1,1,1,1,1,1,1,1]
=> [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]
=> [2,1,1,1,1,1,1,1,1] => ? = 2
[1,1,1,1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
=> [1,1,1,1,1,1,1,1,1,1] => ? = 1
[11]
=> [[1,2,3,4,5,6,7,8,9,10,11]]
=> ? => ? = 1
[10,1]
=> [[1,2,3,4,5,6,7,8,9,10],[11]]
=> ? => ? = 1
[9,2]
=> [[1,2,3,4,5,6,7,8,9],[10,11]]
=> ? => ? = 1
[9,1,1]
=> [[1,2,3,4,5,6,7,8,9],[10],[11]]
=> ? => ? = 2
[8,3]
=> [[1,2,3,4,5,6,7,8],[9,10,11]]
=> ? => ? = 1
[8,2,1]
=> [[1,2,3,4,5,6,7,8],[9,10],[11]]
=> ? => ? = 1
[8,1,1,1]
=> [[1,2,3,4,5,6,7,8],[9],[10],[11]]
=> ? => ? = 2
[7,4]
=> [[1,2,3,4,5,6,7],[8,9,10,11]]
=> ? => ? = 1
Description
The number of different multiplicities of parts of an integer composition.
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