Your data matches 7 different statistics following compositions of up to 3 maps.
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Matching statistic: St000148
(load all 2 compositions to match this statistic)
Mapping
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
St000148: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [1,1]
 => 2
[[2,2]]
 => [2]
 => 0
[[1],[2]]
 => [1,1]
 => 2
[[1,3]]
 => [1,1]
 => 2
[[2,3]]
 => [1,1]
 => 2
[[3,3]]
 => [2]
 => 0
[[1],[3]]
 => [1,1]
 => 2
[[2],[3]]
 => [1,1]
 => 2
[[1,1,2]]
 => [2,1]
 => 1
[[1,2,2]]
 => [2,1]
 => 1
[[2,2,2]]
 => [3]
 => 1
[[1,1],[2]]
 => [2,1]
 => 1
[[1,2],[2]]
 => [2,1]
 => 1
[[1,4]]
 => [1,1]
 => 2
[[2,4]]
 => [1,1]
 => 2
[[3,4]]
 => [1,1]
 => 2
[[4,4]]
 => [2]
 => 0
[[1],[4]]
 => [1,1]
 => 2
[[2],[4]]
 => [1,1]
 => 2
[[3],[4]]
 => [1,1]
 => 2
[[1,1,3]]
 => [2,1]
 => 1
[[1,2,3]]
 => [1,1,1]
 => 3
[[1,3,3]]
 => [2,1]
 => 1
[[2,2,3]]
 => [2,1]
 => 1
[[2,3,3]]
 => [2,1]
 => 1
[[3,3,3]]
 => [3]
 => 1
[[1,1],[3]]
 => [2,1]
 => 1
[[1,2],[3]]
 => [1,1,1]
 => 3
[[1,3],[2]]
 => [1,1,1]
 => 3
[[1,3],[3]]
 => [2,1]
 => 1
[[2,2],[3]]
 => [2,1]
 => 1
[[2,3],[3]]
 => [2,1]
 => 1
[[1],[2],[3]]
 => [1,1,1]
 => 3
[[1,1,1,2]]
 => [3,1]
 => 2
[[1,1,2,2]]
 => [2,2]
 => 0
[[1,2,2,2]]
 => [3,1]
 => 2
[[2,2,2,2]]
 => [4]
 => 0
[[1,1,1],[2]]
 => [3,1]
 => 2
[[1,1,2],[2]]
 => [2,2]
 => 0
[[1,2,2],[2]]
 => [3,1]
 => 2
[[1,1],[2,2]]
 => [2,2]
 => 0
[[1,5]]
 => [1,1]
 => 2
[[2,5]]
 => [1,1]
 => 2
[[3,5]]
 => [1,1]
 => 2
[[4,5]]
 => [1,1]
 => 2
[[5,5]]
 => [2]
 => 0
[[1],[5]]
 => [1,1]
 => 2
[[2],[5]]
 => [1,1]
 => 2
[[3],[5]]
 => [1,1]
 => 2
[[4],[5]]
 => [1,1]
 => 2
Description
The number of odd parts of a partition.
Matching statistic: St000288
(load all 2 compositions to match this statistic)
Mapping
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Mp00317: Integer partitions —odd parts⟶ Binary words
St000288: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [1,1]
 => 11 => 2
[[2,2]]
 => [2]
 => 0 => 0
[[1],[2]]
 => [1,1]
 => 11 => 2
[[1,3]]
 => [1,1]
 => 11 => 2
[[2,3]]
 => [1,1]
 => 11 => 2
[[3,3]]
 => [2]
 => 0 => 0
[[1],[3]]
 => [1,1]
 => 11 => 2
[[2],[3]]
 => [1,1]
 => 11 => 2
[[1,1,2]]
 => [2,1]
 => 01 => 1
[[1,2,2]]
 => [2,1]
 => 01 => 1
[[2,2,2]]
 => [3]
 => 1 => 1
[[1,1],[2]]
 => [2,1]
 => 01 => 1
[[1,2],[2]]
 => [2,1]
 => 01 => 1
[[1,4]]
 => [1,1]
 => 11 => 2
[[2,4]]
 => [1,1]
 => 11 => 2
[[3,4]]
 => [1,1]
 => 11 => 2
[[4,4]]
 => [2]
 => 0 => 0
[[1],[4]]
 => [1,1]
 => 11 => 2
[[2],[4]]
 => [1,1]
 => 11 => 2
[[3],[4]]
 => [1,1]
 => 11 => 2
[[1,1,3]]
 => [2,1]
 => 01 => 1
[[1,2,3]]
 => [1,1,1]
 => 111 => 3
[[1,3,3]]
 => [2,1]
 => 01 => 1
[[2,2,3]]
 => [2,1]
 => 01 => 1
[[2,3,3]]
 => [2,1]
 => 01 => 1
[[3,3,3]]
 => [3]
 => 1 => 1
[[1,1],[3]]
 => [2,1]
 => 01 => 1
[[1,2],[3]]
 => [1,1,1]
 => 111 => 3
[[1,3],[2]]
 => [1,1,1]
 => 111 => 3
[[1,3],[3]]
 => [2,1]
 => 01 => 1
[[2,2],[3]]
 => [2,1]
 => 01 => 1
[[2,3],[3]]
 => [2,1]
 => 01 => 1
[[1],[2],[3]]
 => [1,1,1]
 => 111 => 3
[[1,1,1,2]]
 => [3,1]
 => 11 => 2
[[1,1,2,2]]
 => [2,2]
 => 00 => 0
[[1,2,2,2]]
 => [3,1]
 => 11 => 2
[[2,2,2,2]]
 => [4]
 => 0 => 0
[[1,1,1],[2]]
 => [3,1]
 => 11 => 2
[[1,1,2],[2]]
 => [2,2]
 => 00 => 0
[[1,2,2],[2]]
 => [3,1]
 => 11 => 2
[[1,1],[2,2]]
 => [2,2]
 => 00 => 0
[[1,5]]
 => [1,1]
 => 11 => 2
[[2,5]]
 => [1,1]
 => 11 => 2
[[3,5]]
 => [1,1]
 => 11 => 2
[[4,5]]
 => [1,1]
 => 11 => 2
[[5,5]]
 => [2]
 => 0 => 0
[[1],[5]]
 => [1,1]
 => 11 => 2
[[2],[5]]
 => [1,1]
 => 11 => 2
[[3],[5]]
 => [1,1]
 => 11 => 2
[[4],[5]]
 => [1,1]
 => 11 => 2
Description
The number of ones in a binary word. This is also known as the Hamming weight of the word.
Matching statistic: St000992
(load all 2 compositions to match this statistic)
Mapping
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000992: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [1,1]
 => [2]
 => 2
[[2,2]]
 => [2]
 => [1,1]
 => 0
[[1],[2]]
 => [1,1]
 => [2]
 => 2
[[1,3]]
 => [1,1]
 => [2]
 => 2
[[2,3]]
 => [1,1]
 => [2]
 => 2
[[3,3]]
 => [2]
 => [1,1]
 => 0
[[1],[3]]
 => [1,1]
 => [2]
 => 2
[[2],[3]]
 => [1,1]
 => [2]
 => 2
[[1,1,2]]
 => [2,1]
 => [2,1]
 => 1
[[1,2,2]]
 => [2,1]
 => [2,1]
 => 1
[[2,2,2]]
 => [3]
 => [1,1,1]
 => 1
[[1,1],[2]]
 => [2,1]
 => [2,1]
 => 1
[[1,2],[2]]
 => [2,1]
 => [2,1]
 => 1
[[1,4]]
 => [1,1]
 => [2]
 => 2
[[2,4]]
 => [1,1]
 => [2]
 => 2
[[3,4]]
 => [1,1]
 => [2]
 => 2
[[4,4]]
 => [2]
 => [1,1]
 => 0
[[1],[4]]
 => [1,1]
 => [2]
 => 2
[[2],[4]]
 => [1,1]
 => [2]
 => 2
[[3],[4]]
 => [1,1]
 => [2]
 => 2
[[1,1,3]]
 => [2,1]
 => [2,1]
 => 1
[[1,2,3]]
 => [1,1,1]
 => [3]
 => 3
[[1,3,3]]
 => [2,1]
 => [2,1]
 => 1
[[2,2,3]]
 => [2,1]
 => [2,1]
 => 1
[[2,3,3]]
 => [2,1]
 => [2,1]
 => 1
[[3,3,3]]
 => [3]
 => [1,1,1]
 => 1
[[1,1],[3]]
 => [2,1]
 => [2,1]
 => 1
[[1,2],[3]]
 => [1,1,1]
 => [3]
 => 3
[[1,3],[2]]
 => [1,1,1]
 => [3]
 => 3
[[1,3],[3]]
 => [2,1]
 => [2,1]
 => 1
[[2,2],[3]]
 => [2,1]
 => [2,1]
 => 1
[[2,3],[3]]
 => [2,1]
 => [2,1]
 => 1
[[1],[2],[3]]
 => [1,1,1]
 => [3]
 => 3
[[1,1,1,2]]
 => [3,1]
 => [2,1,1]
 => 2
[[1,1,2,2]]
 => [2,2]
 => [2,2]
 => 0
[[1,2,2,2]]
 => [3,1]
 => [2,1,1]
 => 2
[[2,2,2,2]]
 => [4]
 => [1,1,1,1]
 => 0
[[1,1,1],[2]]
 => [3,1]
 => [2,1,1]
 => 2
[[1,1,2],[2]]
 => [2,2]
 => [2,2]
 => 0
[[1,2,2],[2]]
 => [3,1]
 => [2,1,1]
 => 2
[[1,1],[2,2]]
 => [2,2]
 => [2,2]
 => 0
[[1,5]]
 => [1,1]
 => [2]
 => 2
[[2,5]]
 => [1,1]
 => [2]
 => 2
[[3,5]]
 => [1,1]
 => [2]
 => 2
[[4,5]]
 => [1,1]
 => [2]
 => 2
[[5,5]]
 => [2]
 => [1,1]
 => 0
[[1],[5]]
 => [1,1]
 => [2]
 => 2
[[2],[5]]
 => [1,1]
 => [2]
 => 2
[[3],[5]]
 => [1,1]
 => [2]
 => 2
[[4],[5]]
 => [1,1]
 => [2]
 => 2
Description
The alternating sum of the parts of an integer partition. For a partition $\lambda = (\lambda_1,\ldots,\lambda_k)$, this is $\lambda_1 - \lambda_2 + \cdots \pm \lambda_k$.
Matching statistic: St001372
(load all 2 compositions to match this statistic)
Mapping
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Mp00317: Integer partitions —odd parts⟶ Binary words
St001372: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [1,1]
 => 11 => 2
[[2,2]]
 => [2]
 => 0 => 0
[[1],[2]]
 => [1,1]
 => 11 => 2
[[1,3]]
 => [1,1]
 => 11 => 2
[[2,3]]
 => [1,1]
 => 11 => 2
[[3,3]]
 => [2]
 => 0 => 0
[[1],[3]]
 => [1,1]
 => 11 => 2
[[2],[3]]
 => [1,1]
 => 11 => 2
[[1,1,2]]
 => [2,1]
 => 01 => 1
[[1,2,2]]
 => [2,1]
 => 01 => 1
[[2,2,2]]
 => [3]
 => 1 => 1
[[1,1],[2]]
 => [2,1]
 => 01 => 1
[[1,2],[2]]
 => [2,1]
 => 01 => 1
[[1,4]]
 => [1,1]
 => 11 => 2
[[2,4]]
 => [1,1]
 => 11 => 2
[[3,4]]
 => [1,1]
 => 11 => 2
[[4,4]]
 => [2]
 => 0 => 0
[[1],[4]]
 => [1,1]
 => 11 => 2
[[2],[4]]
 => [1,1]
 => 11 => 2
[[3],[4]]
 => [1,1]
 => 11 => 2
[[1,1,3]]
 => [2,1]
 => 01 => 1
[[1,2,3]]
 => [1,1,1]
 => 111 => 3
[[1,3,3]]
 => [2,1]
 => 01 => 1
[[2,2,3]]
 => [2,1]
 => 01 => 1
[[2,3,3]]
 => [2,1]
 => 01 => 1
[[3,3,3]]
 => [3]
 => 1 => 1
[[1,1],[3]]
 => [2,1]
 => 01 => 1
[[1,2],[3]]
 => [1,1,1]
 => 111 => 3
[[1,3],[2]]
 => [1,1,1]
 => 111 => 3
[[1,3],[3]]
 => [2,1]
 => 01 => 1
[[2,2],[3]]
 => [2,1]
 => 01 => 1
[[2,3],[3]]
 => [2,1]
 => 01 => 1
[[1],[2],[3]]
 => [1,1,1]
 => 111 => 3
[[1,1,1,2]]
 => [3,1]
 => 11 => 2
[[1,1,2,2]]
 => [2,2]
 => 00 => 0
[[1,2,2,2]]
 => [3,1]
 => 11 => 2
[[2,2,2,2]]
 => [4]
 => 0 => 0
[[1,1,1],[2]]
 => [3,1]
 => 11 => 2
[[1,1,2],[2]]
 => [2,2]
 => 00 => 0
[[1,2,2],[2]]
 => [3,1]
 => 11 => 2
[[1,1],[2,2]]
 => [2,2]
 => 00 => 0
[[1,5]]
 => [1,1]
 => 11 => 2
[[2,5]]
 => [1,1]
 => 11 => 2
[[3,5]]
 => [1,1]
 => 11 => 2
[[4,5]]
 => [1,1]
 => 11 => 2
[[5,5]]
 => [2]
 => 0 => 0
[[1],[5]]
 => [1,1]
 => 11 => 2
[[2],[5]]
 => [1,1]
 => 11 => 2
[[3],[5]]
 => [1,1]
 => 11 => 2
[[4],[5]]
 => [1,1]
 => 11 => 2
Description
The length of a longest cyclic run of ones of a binary word. Consider the binary word as a cyclic arrangement of ones and zeros. Then this statistic is the length of the longest continuous sequence of ones in this arrangement.
Matching statistic: St001645
Mapping
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 67%
Values
[[1,2]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2}
[[2,2]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2}
[[1],[2]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[1,3]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2,2}
[[2,3]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2,2}
[[3,3]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2,2}
[[1],[3]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[2],[3]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[1,1,2]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1}
[[1,2,2]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1}
[[2,2,2]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1}
[[1,1],[2]]
 => [3,1,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1}
[[1,2],[2]]
 => [2,1,3] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1}
[[1,4]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2,2,2}
[[2,4]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2,2,2}
[[3,4]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2,2,2}
[[4,4]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2,2,2}
[[1],[4]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[2],[4]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[3],[4]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[1,1,3]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1,2,3]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1,3,3]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[2,2,3]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[2,3,3]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[3,3,3]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1,1],[3]]
 => [3,1,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1,2],[3]]
 => [3,1,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1,3],[2]]
 => [2,1,3] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1,3],[3]]
 => [2,1,3] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[2,2],[3]]
 => [3,1,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[2,3],[3]]
 => [2,1,3] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1],[2],[3]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[1,1,1,2]]
 => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,1,2,2]]
 => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,2,2,2]]
 => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[2,2,2,2]]
 => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,1,1],[2]]
 => [4,1,2,3] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,1,2],[2]]
 => [3,1,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,2,2],[2]]
 => [2,1,3,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,1],[2,2]]
 => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,5]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2,2,2,2}
[[2,5]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2,2,2,2}
[[3,5]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2,2,2,2}
[[4,5]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2,2,2,2}
[[5,5]]
 => [1,2] => [2] => ([],2)
 => ? ∊ {0,2,2,2,2}
[[1],[5]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[2],[5]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[3],[5]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[4],[5]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[1,1,4]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3}
[[1,2,4]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3}
[[1,3,4]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3}
[[1,4,4]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3}
[[2,2,4]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3}
[[2,3,4]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3}
[[2,4,4]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3}
[[3,3,4]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3}
[[3,4,4]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3}
[[4,4,4]]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3}
[[1,1],[4]]
 => [3,1,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3}
[[1],[2],[4]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[1],[3],[4]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[2],[3],[4]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[1],[6]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[2],[6]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[3],[6]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[4],[6]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[5],[6]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[1],[2],[5]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[1],[3],[5]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[1],[4],[5]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[2],[3],[5]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[2],[4],[5]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[3],[4],[5]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[1],[2],[3],[4]]
 => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[[1],[7]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[2],[7]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[3],[7]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[4],[7]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[5],[7]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[6],[7]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[1],[2],[6]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[1],[3],[6]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[1],[4],[6]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[1],[5],[6]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[2],[3],[6]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[2],[4],[6]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[2],[5],[6]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[3],[4],[6]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[3],[5],[6]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[4],[5],[6]]
 => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[[1],[2],[3],[5]]
 => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[[1],[2],[4],[5]]
 => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[[1],[3],[4],[5]]
 => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[[2],[3],[4],[5]]
 => [4,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[[1],[8]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[2],[8]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[3],[8]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
[[4],[8]]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 2
Description
The pebbling number of a connected graph.
Matching statistic: St001880
(load all 4 compositions to match this statistic)
Mapping
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00310: Permutations —toric promotion⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 50%
Values
[[1,2]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2}
[[2,2]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2}
[[1],[2]]
 => [2,1] => [2,1] => ([],2)
 => ? ∊ {0,2,2}
[[1,3]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2,2,2}
[[2,3]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2,2,2}
[[3,3]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2,2,2}
[[1],[3]]
 => [2,1] => [2,1] => ([],2)
 => ? ∊ {0,2,2,2,2}
[[2],[3]]
 => [2,1] => [2,1] => ([],2)
 => ? ∊ {0,2,2,2,2}
[[1,1,2]]
 => [1,2,3] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1}
[[1,2,2]]
 => [1,2,3] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1}
[[2,2,2]]
 => [1,2,3] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1}
[[1,1],[2]]
 => [3,1,2] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,1}
[[1,2],[2]]
 => [2,1,3] => [3,1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1}
[[1,4]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2,2,2,2,2}
[[2,4]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2,2,2,2,2}
[[3,4]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2,2,2,2,2}
[[4,4]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2,2,2,2,2}
[[1],[4]]
 => [2,1] => [2,1] => ([],2)
 => ? ∊ {0,2,2,2,2,2,2}
[[2],[4]]
 => [2,1] => [2,1] => ([],2)
 => ? ∊ {0,2,2,2,2,2,2}
[[3],[4]]
 => [2,1] => [2,1] => ([],2)
 => ? ∊ {0,2,2,2,2,2,2}
[[1,1,3]]
 => [1,2,3] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1,2,3]]
 => [1,2,3] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1,3,3]]
 => [1,2,3] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[2,2,3]]
 => [1,2,3] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[2,3,3]]
 => [1,2,3] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[3,3,3]]
 => [1,2,3] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1,1],[3]]
 => [3,1,2] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1,2],[3]]
 => [3,1,2] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1,3],[2]]
 => [2,1,3] => [3,1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1,3],[3]]
 => [2,1,3] => [3,1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[2,2],[3]]
 => [3,1,2] => [2,1,3] => ([(0,2),(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[2,3],[3]]
 => [2,1,3] => [3,1,2] => ([(1,2)],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3}
[[1],[2],[3]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1,1,1,2]]
 => [1,2,3,4] => [4,2,3,1] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,1,2,2]]
 => [1,2,3,4] => [4,2,3,1] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,2,2,2]]
 => [1,2,3,4] => [4,2,3,1] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[2,2,2,2]]
 => [1,2,3,4] => [4,2,3,1] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,1,1],[2]]
 => [4,1,2,3] => [3,4,2,1] => ([(2,3)],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,1,2],[2]]
 => [3,1,2,4] => [2,4,3,1] => ([(1,2),(1,3)],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,2,2],[2]]
 => [2,1,3,4] => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,1],[2,2]]
 => [3,4,1,2] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,5]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[2,5]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[3,5]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[4,5]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[5,5]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[1],[5]]
 => [2,1] => [2,1] => ([],2)
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[2],[5]]
 => [2,1] => [2,1] => ([],2)
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[3],[5]]
 => [2,1] => [2,1] => ([],2)
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[4],[5]]
 => [2,1] => [2,1] => ([],2)
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[1,1,4]]
 => [1,2,3] => [3,2,1] => ([],3)
 => ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,3,3,3,3}
[[1],[2],[4]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[3],[4]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[2],[3],[4]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[2],[5]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[3],[5]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[4],[5]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[2],[3],[5]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[2],[4],[5]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[3],[4],[5]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[2],[3],[4]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[1],[2],[6]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[3],[6]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[4],[6]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[5],[6]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[2],[3],[6]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[2],[4],[6]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[2],[5],[6]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[3],[4],[6]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[3],[5],[6]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[4],[5],[6]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[2],[3],[5]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[1],[2],[4],[5]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[1],[3],[4],[5]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[2],[3],[4],[5]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[1],[2],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[3],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[4],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[5],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[6],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[2],[3],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[2],[4],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[2],[5],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[2],[6],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[3],[4],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[3],[5],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[3],[6],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[4],[5],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[4],[6],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[5],[6],[7]]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 3
[[1],[2],[3],[6]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[1],[2],[4],[6]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[1],[2],[5],[6]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[1],[3],[4],[6]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[1],[3],[5],[6]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[1],[4],[5],[6]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[2],[3],[4],[6]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[2],[3],[5],[6]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[2],[4],[5],[6]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[[3],[4],[5],[6]]
 => [4,3,2,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001603
Mapping
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 17%
Values
[[1,2]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2}
[[2,2]]
 => [2]
 => []
 => ?
 => ? ∊ {0,2,2}
[[1],[2]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2}
[[1,3]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2}
[[2,3]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2}
[[3,3]]
 => [2]
 => []
 => ?
 => ? ∊ {0,2,2,2,2}
[[1],[3]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2}
[[2],[3]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2}
[[1,1,2]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {1,1,1,1,1}
[[1,2,2]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {1,1,1,1,1}
[[2,2,2]]
 => [3]
 => []
 => ?
 => ? ∊ {1,1,1,1,1}
[[1,1],[2]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {1,1,1,1,1}
[[1,2],[2]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {1,1,1,1,1}
[[1,4]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2}
[[2,4]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2}
[[3,4]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2}
[[4,4]]
 => [2]
 => []
 => ?
 => ? ∊ {0,2,2,2,2,2,2}
[[1],[4]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2}
[[2],[4]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2}
[[3],[4]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2}
[[1,1,3]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[1,2,3]]
 => [1,1,1]
 => [1,1]
 => [1]
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[1,3,3]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[2,2,3]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[2,3,3]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[3,3,3]]
 => [3]
 => []
 => ?
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[1,1],[3]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[1,2],[3]]
 => [1,1,1]
 => [1,1]
 => [1]
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[1,3],[2]]
 => [1,1,1]
 => [1,1]
 => [1]
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[1,3],[3]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[2,2],[3]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[2,3],[3]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[1],[2],[3]]
 => [1,1,1]
 => [1,1]
 => [1]
 => ? ∊ {1,1,1,1,1,1,1,1,1,3,3,3,3}
[[1,1,1,2]]
 => [3,1]
 => [1]
 => []
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,1,2,2]]
 => [2,2]
 => [2]
 => []
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,2,2,2]]
 => [3,1]
 => [1]
 => []
 => ? ∊ {0,0,0,0,2,2,2,2}
[[2,2,2,2]]
 => [4]
 => []
 => ?
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,1,1],[2]]
 => [3,1]
 => [1]
 => []
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,1,2],[2]]
 => [2,2]
 => [2]
 => []
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,2,2],[2]]
 => [3,1]
 => [1]
 => []
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,1],[2,2]]
 => [2,2]
 => [2]
 => []
 => ? ∊ {0,0,0,0,2,2,2,2}
[[1,5]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[2,5]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[3,5]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[4,5]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[5,5]]
 => [2]
 => []
 => ?
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[1],[5]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[2],[5]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[3],[5]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[4],[5]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,2,2,2,2,2,2,2,2}
[[1,2,3,4,5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,2,3,4],[5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,2,3,5],[4]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,2,4,5],[3]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,3,4,5],[2]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,2,3],[4,5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,2,4],[3,5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,2,5],[3,4]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,3,4],[2,5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,3,5],[2,4]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,2,3],[4],[5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,2,4],[3],[5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,2,5],[3],[4]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,3,4],[2],[5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,3,5],[2],[4]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,4,5],[2],[3]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,2],[3,4],[5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,2],[3,5],[4]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,3],[2,4],[5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,3],[2,5],[4]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,4],[2,5],[3]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,2],[3],[4],[5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,3],[2],[4],[5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,4],[2],[3],[5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1,5],[2],[3],[4]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[[1],[2],[3],[4],[5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 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.