Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000089
(load all 2 compositions to match this statistic)
Mapping
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
St000089: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [1] => 0
[[1,2]]
 => [2] => 0
[[1],[2]]
 => [1,1] => 0
[[1,2,3]]
 => [3] => 0
[[1,3],[2]]
 => [1,2] => 1
[[1,2],[3]]
 => [2,1] => 1
[[1],[2],[3]]
 => [1,1,1] => 0
[[1,2,3,4]]
 => [4] => 0
[[1,3,4],[2]]
 => [1,3] => 2
[[1,2,4],[3]]
 => [2,2] => 0
[[1,2,3],[4]]
 => [3,1] => 2
[[1,3],[2,4]]
 => [1,2,1] => 2
[[1,2],[3,4]]
 => [2,2] => 0
[[1,4],[2],[3]]
 => [1,1,2] => 1
[[1,3],[2],[4]]
 => [1,2,1] => 2
[[1,2],[3],[4]]
 => [2,1,1] => 1
[[1],[2],[3],[4]]
 => [1,1,1,1] => 0
[[1,2,3,4,5]]
 => [5] => 0
[[1,3,4,5],[2]]
 => [1,4] => 3
[[1,2,4,5],[3]]
 => [2,3] => 1
[[1,2,3,5],[4]]
 => [3,2] => 1
[[1,2,3,4],[5]]
 => [4,1] => 3
[[1,3,5],[2,4]]
 => [1,2,2] => 1
[[1,2,5],[3,4]]
 => [2,3] => 1
[[1,3,4],[2,5]]
 => [1,3,1] => 4
[[1,2,4],[3,5]]
 => [2,2,1] => 1
[[1,2,3],[4,5]]
 => [3,2] => 1
[[1,4,5],[2],[3]]
 => [1,1,3] => 2
[[1,3,5],[2],[4]]
 => [1,2,2] => 1
[[1,2,5],[3],[4]]
 => [2,1,2] => 2
[[1,3,4],[2],[5]]
 => [1,3,1] => 4
[[1,2,4],[3],[5]]
 => [2,2,1] => 1
[[1,2,3],[4],[5]]
 => [3,1,1] => 2
[[1,4],[2,5],[3]]
 => [1,1,2,1] => 2
[[1,3],[2,5],[4]]
 => [1,2,2] => 1
[[1,2],[3,5],[4]]
 => [2,1,2] => 2
[[1,3],[2,4],[5]]
 => [1,2,1,1] => 2
[[1,2],[3,4],[5]]
 => [2,2,1] => 1
[[1,5],[2],[3],[4]]
 => [1,1,1,2] => 1
[[1,4],[2],[3],[5]]
 => [1,1,2,1] => 2
[[1,3],[2],[4],[5]]
 => [1,2,1,1] => 2
[[1,2],[3],[4],[5]]
 => [2,1,1,1] => 1
[[1],[2],[3],[4],[5]]
 => [1,1,1,1,1] => 0
[[1,2,3,4,5,6]]
 => [6] => 0
[[1,3,4,5,6],[2]]
 => [1,5] => 4
[[1,2,4,5,6],[3]]
 => [2,4] => 2
[[1,2,3,5,6],[4]]
 => [3,3] => 0
[[1,2,3,4,6],[5]]
 => [4,2] => 2
[[1,2,3,4,5],[6]]
 => [5,1] => 4
[[1,3,5,6],[2,4]]
 => [1,2,3] => 2
Description
The absolute variation of a composition.
Matching statistic: St000993
Mapping
Mp00083: Standard tableaux —shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 46% ●values known / values provided: 46%●distinct values known / distinct values provided: 62%
Values
[[1]]
 => [1]
 => []
 => ?
 => ? = 0
[[1,2]]
 => [2]
 => []
 => ?
 => ? ∊ {0,0}
[[1],[2]]
 => [1,1]
 => [1]
 => []
 => ? ∊ {0,0}
[[1,2,3]]
 => [3]
 => []
 => ?
 => ? ∊ {0,0,1,1}
[[1,3],[2]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {0,0,1,1}
[[1,2],[3]]
 => [2,1]
 => [1]
 => []
 => ? ∊ {0,0,1,1}
[[1],[2],[3]]
 => [1,1,1]
 => [1,1]
 => [1]
 => ? ∊ {0,0,1,1}
[[1,2,3,4]]
 => [4]
 => []
 => ?
 => ? ∊ {0,0,0,0,1,1,2,2,2}
[[1,3,4],[2]]
 => [3,1]
 => [1]
 => []
 => ? ∊ {0,0,0,0,1,1,2,2,2}
[[1,2,4],[3]]
 => [3,1]
 => [1]
 => []
 => ? ∊ {0,0,0,0,1,1,2,2,2}
[[1,2,3],[4]]
 => [3,1]
 => [1]
 => []
 => ? ∊ {0,0,0,0,1,1,2,2,2}
[[1,3],[2,4]]
 => [2,2]
 => [2]
 => []
 => ? ∊ {0,0,0,0,1,1,2,2,2}
[[1,2],[3,4]]
 => [2,2]
 => [2]
 => []
 => ? ∊ {0,0,0,0,1,1,2,2,2}
[[1,4],[2],[3]]
 => [2,1,1]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,1,1,2,2,2}
[[1,3],[2],[4]]
 => [2,1,1]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,1,1,2,2,2}
[[1,2],[3],[4]]
 => [2,1,1]
 => [1,1]
 => [1]
 => ? ∊ {0,0,0,0,1,1,2,2,2}
[[1],[2],[3],[4]]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,2,3,4,5]]
 => [5]
 => []
 => ?
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,3,4,5],[2]]
 => [4,1]
 => [1]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,2,4,5],[3]]
 => [4,1]
 => [1]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,2,3,5],[4]]
 => [4,1]
 => [1]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,2,3,4],[5]]
 => [4,1]
 => [1]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,3,5],[2,4]]
 => [3,2]
 => [2]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,2,5],[3,4]]
 => [3,2]
 => [2]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,3,4],[2,5]]
 => [3,2]
 => [2]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,2,4],[3,5]]
 => [3,2]
 => [2]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,2,3],[4,5]]
 => [3,2]
 => [2]
 => []
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,4,5],[2],[3]]
 => [3,1,1]
 => [1,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,3,5],[2],[4]]
 => [3,1,1]
 => [1,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,2,5],[3],[4]]
 => [3,1,1]
 => [1,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,3,4],[2],[5]]
 => [3,1,1]
 => [1,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,2,4],[3],[5]]
 => [3,1,1]
 => [1,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,2,3],[4],[5]]
 => [3,1,1]
 => [1,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,4],[2,5],[3]]
 => [2,2,1]
 => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,3],[2,5],[4]]
 => [2,2,1]
 => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,2],[3,5],[4]]
 => [2,2,1]
 => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,3],[2,4],[5]]
 => [2,2,1]
 => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,2],[3,4],[5]]
 => [2,2,1]
 => [2,1]
 => [1]
 => ? ∊ {0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4}
[[1,5],[2],[3],[4]]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,4],[2],[3],[5]]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,3],[2],[4],[5]]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,2],[3],[4],[5]]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1],[2],[3],[4],[5]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
[[1,2,3,4,5,6]]
 => [6]
 => []
 => ?
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,3,4,5,6],[2]]
 => [5,1]
 => [1]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,2,4,5,6],[3]]
 => [5,1]
 => [1]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,2,3,5,6],[4]]
 => [5,1]
 => [1]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,2,3,4,6],[5]]
 => [5,1]
 => [1]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,2,3,4,5],[6]]
 => [5,1]
 => [1]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,3,5,6],[2,4]]
 => [4,2]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,2,5,6],[3,4]]
 => [4,2]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,3,4,6],[2,5]]
 => [4,2]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,2,4,6],[3,5]]
 => [4,2]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,2,3,6],[4,5]]
 => [4,2]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,3,4,5],[2,6]]
 => [4,2]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,2,4,5],[3,6]]
 => [4,2]
 => [2]
 => []
 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,6,6}
[[1,5,6],[2],[3],[4]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,4,6],[2],[3],[5]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,3,6],[2],[4],[5]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,2,6],[3],[4],[5]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,4,5],[2],[3],[6]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,3,5],[2],[4],[6]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,2,5],[3],[4],[6]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,3,4],[2],[5],[6]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,2,4],[3],[5],[6]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,2,3],[4],[5],[6]]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,4],[2,5],[3,6]]
 => [2,2,2]
 => [2,2]
 => [2]
 => 1
[[1,3],[2,5],[4,6]]
 => [2,2,2]
 => [2,2]
 => [2]
 => 1
[[1,2],[3,5],[4,6]]
 => [2,2,2]
 => [2,2]
 => [2]
 => 1
[[1,3],[2,4],[5,6]]
 => [2,2,2]
 => [2,2]
 => [2]
 => 1
[[1,2],[3,4],[5,6]]
 => [2,2,2]
 => [2,2]
 => [2]
 => 1
[[1,5],[2,6],[3],[4]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
[[1,4],[2,6],[3],[5]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
[[1,3],[2,6],[4],[5]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
[[1,2],[3,6],[4],[5]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
[[1,4],[2,5],[3],[6]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
[[1,3],[2,5],[4],[6]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
[[1,2],[3,5],[4],[6]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
[[1,3],[2,4],[5],[6]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
[[1,2],[3,4],[5],[6]]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
[[1,6],[2],[3],[4],[5]]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
[[1,5],[2],[3],[4],[6]]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
[[1,4],[2],[3],[5],[6]]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
[[1,3],[2],[4],[5],[6]]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
[[1,2],[3],[4],[5],[6]]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
[[1],[2],[3],[4],[5],[6]]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 4
[[1,5,6,7],[2],[3],[4]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,4,6,7],[2],[3],[5]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,3,6,7],[2],[4],[5]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,2,6,7],[3],[4],[5]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,4,5,7],[2],[3],[6]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,3,5,7],[2],[4],[6]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,2,5,7],[3],[4],[6]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,3,4,7],[2],[5],[6]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,2,4,7],[3],[5],[6]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,2,3,7],[4],[5],[6]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,4,5,6],[2],[3],[7]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,3,5,6],[2],[4],[7]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,2,5,6],[3],[4],[7]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
[[1,3,4,6],[2],[5],[7]]
 => [4,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
Description
The multiplicity of the largest part of an integer partition.