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Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St001410
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St001410: Semistandard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
=> 1
[[2,2]]
=> 2
[[1],[2]]
=> 1
[[1,3]]
=> 1
[[2,3]]
=> 2
[[3,3]]
=> 3
[[1],[3]]
=> 1
[[2],[3]]
=> 2
[[1,1,2]]
=> 1
[[1,2,2]]
=> 1
[[2,2,2]]
=> 2
[[1,1],[2]]
=> 1
[[1,2],[2]]
=> 1
[[1,4]]
=> 1
[[2,4]]
=> 2
[[3,4]]
=> 3
[[4,4]]
=> 4
[[1],[4]]
=> 1
[[2],[4]]
=> 2
[[3],[4]]
=> 3
[[1,1,3]]
=> 1
[[1,2,3]]
=> 1
[[1,3,3]]
=> 1
[[2,2,3]]
=> 2
[[2,3,3]]
=> 2
[[3,3,3]]
=> 3
[[1,1],[3]]
=> 1
[[1,2],[3]]
=> 1
[[1,3],[2]]
=> 1
[[1,3],[3]]
=> 1
[[2,2],[3]]
=> 2
[[2,3],[3]]
=> 2
[[1],[2],[3]]
=> 1
[[1,1,1,2]]
=> 1
[[1,1,2,2]]
=> 1
[[1,2,2,2]]
=> 1
[[2,2,2,2]]
=> 2
[[1,1,1],[2]]
=> 1
[[1,1,2],[2]]
=> 1
[[1,2,2],[2]]
=> 1
[[1,1],[2,2]]
=> 1
[[1,5]]
=> 1
[[2,5]]
=> 2
[[3,5]]
=> 3
[[4,5]]
=> 4
[[5,5]]
=> 5
[[1],[5]]
=> 1
[[2],[5]]
=> 2
[[3],[5]]
=> 3
[[4],[5]]
=> 4
Description
The minimal entry of a semistandard tableau.
Matching statistic: St000170
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux
St000170: Semistandard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000170: Semistandard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
=> [[1,2]]
=> 1
[[2,2]]
=> [[2,2]]
=> 2
[[1],[2]]
=> [[1,2]]
=> 1
[[1,3]]
=> [[1,3]]
=> 1
[[2,3]]
=> [[2,3]]
=> 2
[[3,3]]
=> [[3,3]]
=> 3
[[1],[3]]
=> [[1,3]]
=> 1
[[2],[3]]
=> [[2,3]]
=> 2
[[1,1,2]]
=> [[1,1,2]]
=> 1
[[1,2,2]]
=> [[1,2,2]]
=> 1
[[2,2,2]]
=> [[2,2,2]]
=> 2
[[1,1],[2]]
=> [[1,1,2]]
=> 1
[[1,2],[2]]
=> [[1,2,2]]
=> 1
[[1,4]]
=> [[1,4]]
=> 1
[[2,4]]
=> [[2,4]]
=> 2
[[3,4]]
=> [[3,4]]
=> 3
[[4,4]]
=> [[4,4]]
=> 4
[[1],[4]]
=> [[1,4]]
=> 1
[[2],[4]]
=> [[2,4]]
=> 2
[[3],[4]]
=> [[3,4]]
=> 3
[[1,1,3]]
=> [[1,1,3]]
=> 1
[[1,2,3]]
=> [[1,2,3]]
=> 1
[[1,3,3]]
=> [[1,3,3]]
=> 1
[[2,2,3]]
=> [[2,2,3]]
=> 2
[[2,3,3]]
=> [[2,3,3]]
=> 2
[[3,3,3]]
=> [[3,3,3]]
=> 3
[[1,1],[3]]
=> [[1,1,3]]
=> 1
[[1,2],[3]]
=> [[1,2,3]]
=> 1
[[1,3],[2]]
=> [[1,2],[3]]
=> 1
[[1,3],[3]]
=> [[1,3,3]]
=> 1
[[2,2],[3]]
=> [[2,2,3]]
=> 2
[[2,3],[3]]
=> [[2,3,3]]
=> 2
[[1],[2],[3]]
=> [[1,2],[3]]
=> 1
[[1,1,1,2]]
=> [[1,1,1,2]]
=> 1
[[1,1,2,2]]
=> [[1,1,2,2]]
=> 1
[[1,2,2,2]]
=> [[1,2,2,2]]
=> 1
[[2,2,2,2]]
=> [[2,2,2,2]]
=> 2
[[1,1,1],[2]]
=> [[1,1,1,2]]
=> 1
[[1,1,2],[2]]
=> [[1,1,2,2]]
=> 1
[[1,2,2],[2]]
=> [[1,2,2,2]]
=> 1
[[1,1],[2,2]]
=> [[1,1,2,2]]
=> 1
[[1,5]]
=> [[1,5]]
=> 1
[[2,5]]
=> [[2,5]]
=> 2
[[3,5]]
=> [[3,5]]
=> 3
[[4,5]]
=> [[4,5]]
=> 4
[[5,5]]
=> [[5,5]]
=> 5
[[1],[5]]
=> [[1,5]]
=> 1
[[2],[5]]
=> [[2,5]]
=> 2
[[3],[5]]
=> [[3,5]]
=> 3
[[4],[5]]
=> [[4,5]]
=> 4
Description
The trace of a semistandard tableau.
This is the sum of the entries on the diagonal.
Matching statistic: St000737
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux
St000737: Semistandard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000737: Semistandard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
=> [[1,2]]
=> 1
[[2,2]]
=> [[2,2]]
=> 2
[[1],[2]]
=> [[1,2]]
=> 1
[[1,3]]
=> [[1,3]]
=> 1
[[2,3]]
=> [[2,3]]
=> 2
[[3,3]]
=> [[3,3]]
=> 3
[[1],[3]]
=> [[1,3]]
=> 1
[[2],[3]]
=> [[2,3]]
=> 2
[[1,1,2]]
=> [[1,1,2]]
=> 1
[[1,2,2]]
=> [[1,2,2]]
=> 1
[[2,2,2]]
=> [[2,2,2]]
=> 2
[[1,1],[2]]
=> [[1,1,2]]
=> 1
[[1,2],[2]]
=> [[1,2,2]]
=> 1
[[1,4]]
=> [[1,4]]
=> 1
[[2,4]]
=> [[2,4]]
=> 2
[[3,4]]
=> [[3,4]]
=> 3
[[4,4]]
=> [[4,4]]
=> 4
[[1],[4]]
=> [[1,4]]
=> 1
[[2],[4]]
=> [[2,4]]
=> 2
[[3],[4]]
=> [[3,4]]
=> 3
[[1,1,3]]
=> [[1,1,3]]
=> 1
[[1,2,3]]
=> [[1,2,3]]
=> 1
[[1,3,3]]
=> [[1,3,3]]
=> 1
[[2,2,3]]
=> [[2,2,3]]
=> 2
[[2,3,3]]
=> [[2,3,3]]
=> 2
[[3,3,3]]
=> [[3,3,3]]
=> 3
[[1,1],[3]]
=> [[1,1,3]]
=> 1
[[1,2],[3]]
=> [[1,2,3]]
=> 1
[[1,3],[2]]
=> [[1,2],[3]]
=> 1
[[1,3],[3]]
=> [[1,3,3]]
=> 1
[[2,2],[3]]
=> [[2,2,3]]
=> 2
[[2,3],[3]]
=> [[2,3,3]]
=> 2
[[1],[2],[3]]
=> [[1,2],[3]]
=> 1
[[1,1,1,2]]
=> [[1,1,1,2]]
=> 1
[[1,1,2,2]]
=> [[1,1,2,2]]
=> 1
[[1,2,2,2]]
=> [[1,2,2,2]]
=> 1
[[2,2,2,2]]
=> [[2,2,2,2]]
=> 2
[[1,1,1],[2]]
=> [[1,1,1,2]]
=> 1
[[1,1,2],[2]]
=> [[1,1,2,2]]
=> 1
[[1,2,2],[2]]
=> [[1,2,2,2]]
=> 1
[[1,1],[2,2]]
=> [[1,1,2,2]]
=> 1
[[1,5]]
=> [[1,5]]
=> 1
[[2,5]]
=> [[2,5]]
=> 2
[[3,5]]
=> [[3,5]]
=> 3
[[4,5]]
=> [[4,5]]
=> 4
[[5,5]]
=> [[5,5]]
=> 5
[[1],[5]]
=> [[1,5]]
=> 1
[[2],[5]]
=> [[2,5]]
=> 2
[[3],[5]]
=> [[3,5]]
=> 3
[[4],[5]]
=> [[4,5]]
=> 4
Description
The last entry on the main diagonal of a semistandard tableau.
Matching statistic: St000739
Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux
Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux
Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux
St000739: Semistandard tableaux ⟶ ℤResult quality: 67% ●values known / values provided: 69%●distinct values known / distinct values provided: 67%
Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux
Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux
St000739: Semistandard tableaux ⟶ ℤResult quality: 67% ●values known / values provided: 69%●distinct values known / distinct values provided: 67%
Values
[[1,2]]
=> [[1,2]]
=> [[1,2]]
=> [[1,2]]
=> 1
[[2,2]]
=> [[2,2]]
=> [[2,2]]
=> [[2,2]]
=> 2
[[1],[2]]
=> [[1,2]]
=> [[1,2]]
=> [[1,2]]
=> 1
[[1,3]]
=> [[1,3]]
=> [[1,3]]
=> [[1,3]]
=> ? = 1
[[2,3]]
=> [[2,3]]
=> [[2,3]]
=> [[2,3]]
=> ? = 2
[[3,3]]
=> [[3,3]]
=> [[3,3]]
=> [[3,3]]
=> ? = 3
[[1],[3]]
=> [[1,3]]
=> [[1,3]]
=> [[1,3]]
=> ? = 1
[[2],[3]]
=> [[2,3]]
=> [[2,3]]
=> [[2,3]]
=> ? = 2
[[1,1,2]]
=> [[1,1,2]]
=> [[1,1,2]]
=> [[1,1,2]]
=> 1
[[1,2,2]]
=> [[1,2,2]]
=> [[1,2,2]]
=> [[1,2,2]]
=> 1
[[2,2,2]]
=> [[2,2,2]]
=> [[2,2,2]]
=> [[2,2,2]]
=> 2
[[1,1],[2]]
=> [[1,1,2]]
=> [[1,1,2]]
=> [[1,1,2]]
=> 1
[[1,2],[2]]
=> [[1,2,2]]
=> [[1,2,2]]
=> [[1,2,2]]
=> 1
[[1,4]]
=> [[1,4]]
=> [[1,4]]
=> [[1,4]]
=> ? = 1
[[2,4]]
=> [[2,4]]
=> [[2,4]]
=> [[2,4]]
=> ? = 2
[[3,4]]
=> [[3,4]]
=> [[3,4]]
=> [[3,4]]
=> ? = 3
[[4,4]]
=> [[4,4]]
=> [[4,4]]
=> [[4,4]]
=> ? = 4
[[1],[4]]
=> [[1,4]]
=> [[1,4]]
=> [[1,4]]
=> ? = 1
[[2],[4]]
=> [[2,4]]
=> [[2,4]]
=> [[2,4]]
=> ? = 2
[[3],[4]]
=> [[3,4]]
=> [[3,4]]
=> [[3,4]]
=> ? = 3
[[1,1,3]]
=> [[1,1,3]]
=> [[1,1,3]]
=> [[1,1,3]]
=> 1
[[1,2,3]]
=> [[1,2,3]]
=> [[1,2,3]]
=> [[1,2,3]]
=> 1
[[1,3,3]]
=> [[1,3,3]]
=> [[1,3,3]]
=> [[1,3,3]]
=> 1
[[2,2,3]]
=> [[2,2,3]]
=> [[2,2,3]]
=> [[2,2,3]]
=> 2
[[2,3,3]]
=> [[2,3,3]]
=> [[2,3,3]]
=> [[2,3,3]]
=> 2
[[3,3,3]]
=> [[3,3,3]]
=> [[3,3,3]]
=> [[3,3,3]]
=> 3
[[1,1],[3]]
=> [[1,1,3]]
=> [[1,1,3]]
=> [[1,1,3]]
=> 1
[[1,2],[3]]
=> [[1,2,3]]
=> [[1,2,3]]
=> [[1,2,3]]
=> 1
[[1,3],[2]]
=> [[1,2],[3]]
=> [[1,2,3]]
=> [[1,2,3]]
=> 1
[[1,3],[3]]
=> [[1,3,3]]
=> [[1,3,3]]
=> [[1,3,3]]
=> 1
[[2,2],[3]]
=> [[2,2,3]]
=> [[2,2,3]]
=> [[2,2,3]]
=> 2
[[2,3],[3]]
=> [[2,3,3]]
=> [[2,3,3]]
=> [[2,3,3]]
=> 2
[[1],[2],[3]]
=> [[1,2],[3]]
=> [[1,2,3]]
=> [[1,2,3]]
=> 1
[[1,1,1,2]]
=> [[1,1,1,2]]
=> [[1,1,1,2]]
=> [[1,1,1,2]]
=> 1
[[1,1,2,2]]
=> [[1,1,2,2]]
=> [[1,1,2,2]]
=> [[1,1,2,2]]
=> 1
[[1,2,2,2]]
=> [[1,2,2,2]]
=> [[1,2,2,2]]
=> [[1,2,2,2]]
=> 1
[[2,2,2,2]]
=> [[2,2,2,2]]
=> [[2,2,2,2]]
=> [[2,2,2,2]]
=> 2
[[1,1,1],[2]]
=> [[1,1,1,2]]
=> [[1,1,1,2]]
=> [[1,1,1,2]]
=> 1
[[1,1,2],[2]]
=> [[1,1,2,2]]
=> [[1,1,2,2]]
=> [[1,1,2,2]]
=> 1
[[1,2,2],[2]]
=> [[1,2,2,2]]
=> [[1,2,2,2]]
=> [[1,2,2,2]]
=> 1
[[1,1],[2,2]]
=> [[1,1,2,2]]
=> [[1,1,2,2]]
=> [[1,1,2,2]]
=> 1
[[1,5]]
=> [[1,5]]
=> [[1,5]]
=> [[1,5]]
=> ? = 1
[[2,5]]
=> [[2,5]]
=> [[2,5]]
=> [[2,5]]
=> ? = 2
[[3,5]]
=> [[3,5]]
=> [[3,5]]
=> [[3,5]]
=> ? = 3
[[4,5]]
=> [[4,5]]
=> [[4,5]]
=> [[4,5]]
=> ? = 4
[[5,5]]
=> [[5,5]]
=> [[5,5]]
=> [[5,5]]
=> ? = 5
[[1],[5]]
=> [[1,5]]
=> [[1,5]]
=> [[1,5]]
=> ? = 1
[[2],[5]]
=> [[2,5]]
=> [[2,5]]
=> [[2,5]]
=> ? = 2
[[3],[5]]
=> [[3,5]]
=> [[3,5]]
=> [[3,5]]
=> ? = 3
[[4],[5]]
=> [[4,5]]
=> [[4,5]]
=> [[4,5]]
=> ? = 4
[[1,1,4]]
=> [[1,1,4]]
=> [[1,1,4]]
=> [[1,1,4]]
=> ? = 1
[[1,2,4]]
=> [[1,2,4]]
=> [[1,2,4]]
=> [[1,2,4]]
=> ? = 1
[[1,3,4]]
=> [[1,3,4]]
=> [[1,3,4]]
=> [[1,3,4]]
=> ? = 1
[[1,4,4]]
=> [[1,4,4]]
=> [[1,4,4]]
=> [[1,4,4]]
=> ? = 1
[[2,2,4]]
=> [[2,2,4]]
=> [[2,2,4]]
=> [[2,2,4]]
=> ? = 2
[[2,3,4]]
=> [[2,3,4]]
=> [[2,3,4]]
=> [[2,3,4]]
=> ? = 2
[[2,4,4]]
=> [[2,4,4]]
=> [[2,4,4]]
=> [[2,4,4]]
=> ? = 2
[[3,3,4]]
=> [[3,3,4]]
=> [[3,3,4]]
=> [[3,3,4]]
=> ? = 3
[[3,4,4]]
=> [[3,4,4]]
=> [[3,4,4]]
=> [[3,4,4]]
=> ? = 3
[[4,4,4]]
=> [[4,4,4]]
=> [[4,4,4]]
=> [[4,4,4]]
=> ? = 4
[[1,1],[4]]
=> [[1,1,4]]
=> [[1,1,4]]
=> [[1,1,4]]
=> ? = 1
[[1,2],[4]]
=> [[1,2,4]]
=> [[1,2,4]]
=> [[1,2,4]]
=> ? = 1
[[1,4],[2]]
=> [[1,2],[4]]
=> [[1,2,4]]
=> [[1,2,4]]
=> ? = 1
[[1,3],[4]]
=> [[1,3,4]]
=> [[1,3,4]]
=> [[1,3,4]]
=> ? = 1
[[1,4],[3]]
=> [[1,3],[4]]
=> [[1,3,4]]
=> [[1,3,4]]
=> ? = 1
[[1,4],[4]]
=> [[1,4,4]]
=> [[1,4,4]]
=> [[1,4,4]]
=> ? = 1
[[2,2],[4]]
=> [[2,2,4]]
=> [[2,2,4]]
=> [[2,2,4]]
=> ? = 2
[[2,3],[4]]
=> [[2,3,4]]
=> [[2,3,4]]
=> [[2,3,4]]
=> ? = 2
[[2,4],[3]]
=> [[2,3],[4]]
=> [[2,3,4]]
=> [[2,3,4]]
=> ? = 2
[[2,4],[4]]
=> [[2,4,4]]
=> [[2,4,4]]
=> [[2,4,4]]
=> ? = 2
[[3,3],[4]]
=> [[3,3,4]]
=> [[3,3,4]]
=> [[3,3,4]]
=> ? = 3
[[3,4],[4]]
=> [[3,4,4]]
=> [[3,4,4]]
=> [[3,4,4]]
=> ? = 3
[[1],[2],[4]]
=> [[1,2],[4]]
=> [[1,2,4]]
=> [[1,2,4]]
=> ? = 1
[[1],[3],[4]]
=> [[1,3],[4]]
=> [[1,3,4]]
=> [[1,3,4]]
=> ? = 1
[[2],[3],[4]]
=> [[2,3],[4]]
=> [[2,3,4]]
=> [[2,3,4]]
=> ? = 2
[[1,1,1,3]]
=> [[1,1,1,3]]
=> [[1,1,1,3]]
=> [[1,1,1,3]]
=> 1
[[1,1,2,3]]
=> [[1,1,2,3]]
=> [[1,1,2,3]]
=> [[1,1,2,3]]
=> 1
[[1,1,3,3]]
=> [[1,1,3,3]]
=> [[1,1,3,3]]
=> [[1,1,3,3]]
=> 1
[[1,2,2,3]]
=> [[1,2,2,3]]
=> [[1,2,2,3]]
=> [[1,2,2,3]]
=> 1
[[1,2,3,3]]
=> [[1,2,3,3]]
=> [[1,2,3,3]]
=> [[1,2,3,3]]
=> 1
[[1,3,3,3]]
=> [[1,3,3,3]]
=> [[1,3,3,3]]
=> [[1,3,3,3]]
=> 1
[[2,2,2,3]]
=> [[2,2,2,3]]
=> [[2,2,2,3]]
=> [[2,2,2,3]]
=> 2
[[2,2,3,3]]
=> [[2,2,3,3]]
=> [[2,2,3,3]]
=> [[2,2,3,3]]
=> 2
[[2,3,3,3]]
=> [[2,3,3,3]]
=> [[2,3,3,3]]
=> [[2,3,3,3]]
=> 2
[[3,3,3,3]]
=> [[3,3,3,3]]
=> [[3,3,3,3]]
=> [[3,3,3,3]]
=> 3
[[1,1,1],[3]]
=> [[1,1,1,3]]
=> [[1,1,1,3]]
=> [[1,1,1,3]]
=> 1
[[1,1,2],[3]]
=> [[1,1,2,3]]
=> [[1,1,2,3]]
=> [[1,1,2,3]]
=> 1
[[1,1,3],[2]]
=> [[1,1,2],[3]]
=> [[1,1,2,3]]
=> [[1,1,2,3]]
=> 1
[[1,1,3],[3]]
=> [[1,1,3,3]]
=> [[1,1,3,3]]
=> [[1,1,3,3]]
=> 1
[[1,2,2],[3]]
=> [[1,2,2,3]]
=> [[1,2,2,3]]
=> [[1,2,2,3]]
=> 1
[[1,2,3],[2]]
=> [[1,2,2],[3]]
=> [[1,2,2,3]]
=> [[1,2,2,3]]
=> 1
[[1,2,3],[3]]
=> [[1,2,3,3]]
=> [[1,2,3,3]]
=> [[1,2,3,3]]
=> 1
[[1,3,3],[2]]
=> [[1,2,3],[3]]
=> [[1,2,3,3]]
=> [[1,2,3,3]]
=> 1
[[1,3,3],[3]]
=> [[1,3,3,3]]
=> [[1,3,3,3]]
=> [[1,3,3,3]]
=> 1
[[2,2,2],[3]]
=> [[2,2,2,3]]
=> [[2,2,2,3]]
=> [[2,2,2,3]]
=> 2
[[2,2,3],[3]]
=> [[2,2,3,3]]
=> [[2,2,3,3]]
=> [[2,2,3,3]]
=> 2
[[1,6]]
=> [[1,6]]
=> [[1,6]]
=> [[1,6]]
=> ? = 1
[[2,6]]
=> [[2,6]]
=> [[2,6]]
=> [[2,6]]
=> ? = 2
[[3,6]]
=> [[3,6]]
=> [[3,6]]
=> [[3,6]]
=> ? = 3
[[4,6]]
=> [[4,6]]
=> [[4,6]]
=> [[4,6]]
=> ? = 4
Description
The first entry in the last row of a semistandard tableau.
Matching statistic: St001603
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 17%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 17%
Values
[[1,2]]
=> [1,1]
=> [1]
=> ? = 1
[[2,2]]
=> [2]
=> []
=> ? = 2
[[1],[2]]
=> [1,1]
=> [1]
=> ? = 1
[[1,3]]
=> [1,1]
=> [1]
=> ? = 1
[[2,3]]
=> [1,1]
=> [1]
=> ? = 2
[[3,3]]
=> [2]
=> []
=> ? = 3
[[1],[3]]
=> [1,1]
=> [1]
=> ? = 1
[[2],[3]]
=> [1,1]
=> [1]
=> ? = 2
[[1,1,2]]
=> [2,1]
=> [1]
=> ? = 1
[[1,2,2]]
=> [2,1]
=> [1]
=> ? = 1
[[2,2,2]]
=> [3]
=> []
=> ? = 2
[[1,1],[2]]
=> [2,1]
=> [1]
=> ? = 1
[[1,2],[2]]
=> [2,1]
=> [1]
=> ? = 1
[[1,4]]
=> [1,1]
=> [1]
=> ? = 1
[[2,4]]
=> [1,1]
=> [1]
=> ? = 2
[[3,4]]
=> [1,1]
=> [1]
=> ? = 3
[[4,4]]
=> [2]
=> []
=> ? = 4
[[1],[4]]
=> [1,1]
=> [1]
=> ? = 1
[[2],[4]]
=> [1,1]
=> [1]
=> ? = 2
[[3],[4]]
=> [1,1]
=> [1]
=> ? = 3
[[1,1,3]]
=> [2,1]
=> [1]
=> ? = 1
[[1,2,3]]
=> [1,1,1]
=> [1,1]
=> ? = 1
[[1,3,3]]
=> [2,1]
=> [1]
=> ? = 1
[[2,2,3]]
=> [2,1]
=> [1]
=> ? = 2
[[2,3,3]]
=> [2,1]
=> [1]
=> ? = 2
[[3,3,3]]
=> [3]
=> []
=> ? = 3
[[1,1],[3]]
=> [2,1]
=> [1]
=> ? = 1
[[1,2],[3]]
=> [1,1,1]
=> [1,1]
=> ? = 1
[[1,3],[2]]
=> [1,1,1]
=> [1,1]
=> ? = 1
[[1,3],[3]]
=> [2,1]
=> [1]
=> ? = 1
[[2,2],[3]]
=> [2,1]
=> [1]
=> ? = 2
[[2,3],[3]]
=> [2,1]
=> [1]
=> ? = 2
[[1],[2],[3]]
=> [1,1,1]
=> [1,1]
=> ? = 1
[[1,1,1,2]]
=> [3,1]
=> [1]
=> ? = 1
[[1,1,2,2]]
=> [2,2]
=> [2]
=> ? = 1
[[1,2,2,2]]
=> [3,1]
=> [1]
=> ? = 1
[[2,2,2,2]]
=> [4]
=> []
=> ? = 2
[[1,1,1],[2]]
=> [3,1]
=> [1]
=> ? = 1
[[1,1,2],[2]]
=> [2,2]
=> [2]
=> ? = 1
[[1,2,2],[2]]
=> [3,1]
=> [1]
=> ? = 1
[[1,1],[2,2]]
=> [2,2]
=> [2]
=> ? = 1
[[1,5]]
=> [1,1]
=> [1]
=> ? = 1
[[2,5]]
=> [1,1]
=> [1]
=> ? = 2
[[3,5]]
=> [1,1]
=> [1]
=> ? = 3
[[4,5]]
=> [1,1]
=> [1]
=> ? = 4
[[5,5]]
=> [2]
=> []
=> ? = 5
[[1],[5]]
=> [1,1]
=> [1]
=> ? = 1
[[2],[5]]
=> [1,1]
=> [1]
=> ? = 2
[[3],[5]]
=> [1,1]
=> [1]
=> ? = 3
[[4],[5]]
=> [1,1]
=> [1]
=> ? = 4
[[1,2,3,4]]
=> [1,1,1,1]
=> [1,1,1]
=> 1
[[1,2,3],[4]]
=> [1,1,1,1]
=> [1,1,1]
=> 1
[[1,2,4],[3]]
=> [1,1,1,1]
=> [1,1,1]
=> 1
[[1,3,4],[2]]
=> [1,1,1,1]
=> [1,1,1]
=> 1
[[1,2],[3,4]]
=> [1,1,1,1]
=> [1,1,1]
=> 1
[[1,3],[2,4]]
=> [1,1,1,1]
=> [1,1,1]
=> 1
[[1,2],[3],[4]]
=> [1,1,1,1]
=> [1,1,1]
=> 1
[[1,3],[2],[4]]
=> [1,1,1,1]
=> [1,1,1]
=> 1
[[1,4],[2],[3]]
=> [1,1,1,1]
=> [1,1,1]
=> 1
[[1],[2],[3],[4]]
=> [1,1,1,1]
=> [1,1,1]
=> 1
[[1,1,2,2,3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1,2,3,3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,2,2,3,3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1,2,2],[3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1,2,3],[2]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1,2,3],[3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1,3,3],[2]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,2,2,3],[3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,2,3,3],[2]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1,2],[2,3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1,3],[2,2]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1,2],[3,3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1,3],[2,3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,2,2],[3,3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,2,3],[2,3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1,2],[2],[3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1,3],[2],[3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,2,3],[2],[3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1],[2,2],[3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1],[2,3],[3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,2],[2,3],[3]]
=> [2,2,1]
=> [2,1]
=> 1
[[1,1,1,2,2,2]]
=> [3,3]
=> [3]
=> 1
[[1,1,1,2,2],[2]]
=> [3,3]
=> [3]
=> 1
[[1,1,1,2],[2,2]]
=> [3,3]
=> [3]
=> 1
[[1,1,1],[2,2,2]]
=> [3,3]
=> [3]
=> 1
Description
The number of colourings of a polygon such that the multiplicities of a colour are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
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