Your data matches 123 different statistics following compositions of up to 3 maps.
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Mp00024: Dyck paths to 321-avoiding permutationPermutations
Mp00086: Permutations first fundamental transformationPermutations
Mp00204: Permutations LLPSInteger partitions
St000993: Integer partitions ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
=> [2,1] => [2,1] => [2]
=> 1
[1,1,0,0]
=> [1,2] => [1,2] => [1,1]
=> 2
[1,0,1,0,1,0]
=> [2,1,3] => [2,1,3] => [2,1]
=> 1
[1,0,1,1,0,0]
=> [2,3,1] => [3,2,1] => [3]
=> 1
[1,1,0,0,1,0]
=> [3,1,2] => [2,3,1] => [2,1]
=> 1
[1,1,0,1,0,0]
=> [1,3,2] => [1,3,2] => [2,1]
=> 1
[1,1,1,0,0,0]
=> [1,2,3] => [1,2,3] => [1,1,1]
=> 3
[1,0,1,0,1,0,1,0]
=> [2,1,4,3] => [2,1,4,3] => [2,2]
=> 2
[1,0,1,0,1,1,0,0]
=> [2,4,1,3] => [3,2,4,1] => [3,1]
=> 1
[1,0,1,1,0,0,1,0]
=> [2,1,3,4] => [2,1,3,4] => [2,1,1]
=> 1
[1,0,1,1,0,1,0,0]
=> [2,3,1,4] => [3,2,1,4] => [3,1]
=> 1
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [4,2,3,1] => [3,1]
=> 1
[1,1,0,0,1,0,1,0]
=> [3,1,4,2] => [3,4,1,2] => [2,1,1]
=> 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [2,4,3,1] => [3,1]
=> 1
[1,1,0,1,0,0,1,0]
=> [3,1,2,4] => [2,3,1,4] => [2,1,1]
=> 1
[1,1,0,1,0,1,0,0]
=> [1,3,2,4] => [1,3,2,4] => [2,1,1]
=> 1
[1,1,0,1,1,0,0,0]
=> [1,3,4,2] => [1,4,3,2] => [3,1]
=> 1
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [2,3,4,1] => [2,1,1]
=> 1
[1,1,1,0,0,1,0,0]
=> [1,4,2,3] => [1,3,4,2] => [2,1,1]
=> 1
[1,1,1,0,1,0,0,0]
=> [1,2,4,3] => [1,2,4,3] => [2,1,1]
=> 1
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> 4
[1,0,1,0,1,0,1,0,1,0]
=> [2,1,4,3,5] => [2,1,4,3,5] => [2,2,1]
=> 2
[1,0,1,0,1,0,1,1,0,0]
=> [2,4,1,3,5] => [3,2,4,1,5] => [3,1,1]
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> [2,1,4,5,3] => [2,1,5,4,3] => [3,2]
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [2,4,1,5,3] => [4,2,5,1,3] => [3,1,1]
=> 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,4,5,1,3] => [3,2,5,4,1] => [3,2]
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,5,3,4] => [2,1,4,5,3] => [2,2,1]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [2,5,1,3,4] => [3,2,4,5,1] => [3,1,1]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [2,1,3,5,4] => [2,1,3,5,4] => [2,2,1]
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [2,3,1,5,4] => [3,2,1,5,4] => [3,2]
=> 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => [4,2,3,5,1] => [3,1,1]
=> 1
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,4,5] => [2,1,3,4,5] => [2,1,1,1]
=> 1
[1,0,1,1,1,0,0,1,0,0]
=> [2,3,1,4,5] => [3,2,1,4,5] => [3,1,1]
=> 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,3,4,1,5] => [4,2,3,1,5] => [3,1,1]
=> 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [5,2,3,4,1] => [3,1,1]
=> 1
[1,1,0,0,1,0,1,0,1,0]
=> [3,1,4,2,5] => [3,4,1,2,5] => [2,1,1,1]
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [3,4,1,2,5] => [2,4,3,1,5] => [3,1,1]
=> 1
[1,1,0,0,1,1,0,0,1,0]
=> [3,1,4,5,2] => [3,5,1,4,2] => [3,1,1]
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [3,4,1,5,2] => [4,5,3,1,2] => [3,1,1]
=> 1
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [2,5,3,4,1] => [3,1,1]
=> 1
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,5,2,4] => [3,4,1,5,2] => [2,2,1]
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,5,1,2,4] => [2,4,3,5,1] => [3,1,1]
=> 1
[1,1,0,1,0,1,0,0,1,0]
=> [3,1,2,5,4] => [2,3,1,5,4] => [2,2,1]
=> 2
[1,1,0,1,0,1,0,1,0,0]
=> [1,3,2,5,4] => [1,3,2,5,4] => [2,2,1]
=> 2
[1,1,0,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => [1,4,3,5,2] => [3,1,1]
=> 1
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,4,5] => [2,3,1,4,5] => [2,1,1,1]
=> 1
[1,1,0,1,1,0,0,1,0,0]
=> [1,3,2,4,5] => [1,3,2,4,5] => [2,1,1,1]
=> 1
[1,1,0,1,1,0,1,0,0,0]
=> [1,3,4,2,5] => [1,4,3,2,5] => [3,1,1]
=> 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,3,4,5,2] => [1,5,3,4,2] => [3,1,1]
=> 1
[1,1,1,0,0,0,1,0,1,0]
=> [4,1,5,2,3] => [4,3,5,1,2] => [3,1,1]
=> 1
Description
The multiplicity of the largest part of an integer partition.
Mp00201: Dyck paths RingelPermutations
Mp00060: Permutations Robinson-Schensted tableau shapeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001603: Integer partitions ⟶ ℤResult quality: 29% values known / values provided: 84%distinct values known / distinct values provided: 29%
Values
[1,0,1,0]
=> [3,1,2] => [2,1]
=> [1]
=> ? ∊ {1,2}
[1,1,0,0]
=> [2,3,1] => [2,1]
=> [1]
=> ? ∊ {1,2}
[1,0,1,0,1,0]
=> [4,1,2,3] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,3}
[1,0,1,1,0,0]
=> [3,1,4,2] => [2,2]
=> [2]
=> ? ∊ {1,1,1,1,3}
[1,1,0,0,1,0]
=> [2,4,1,3] => [2,2]
=> [2]
=> ? ∊ {1,1,1,1,3}
[1,1,0,1,0,0]
=> [4,3,1,2] => [2,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,3}
[1,1,1,0,0,0]
=> [2,3,4,1] => [3,1]
=> [1]
=> ? ∊ {1,1,1,1,3}
[1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,4}
[1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => [3,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,4}
[1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => [3,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,4}
[1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => [3,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,4}
[1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => [3,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,4}
[1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => [3,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,4}
[1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => [3,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,4}
[1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => [3,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,4}
[1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => [3,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,4}
[1,1,0,1,1,0,0,0]
=> [4,3,1,5,2] => [2,2,1]
=> [2,1]
=> 1
[1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => [3,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,4}
[1,1,1,0,0,1,0,0]
=> [2,5,4,1,3] => [2,2,1]
=> [2,1]
=> 1
[1,1,1,0,1,0,0,0]
=> [5,3,4,1,2] => [2,2,1]
=> [2,1]
=> 1
[1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [4,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,4}
[1,0,1,0,1,0,1,0,1,0]
=> [6,1,2,3,4,5] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,0,1,1,0,0]
=> [5,1,2,3,6,4] => [4,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,1,0,0,1,0]
=> [4,1,2,6,3,5] => [4,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => [4,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => [4,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,1,0,0,1,0,1,0]
=> [3,1,6,2,4,5] => [4,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,1,0,0,1,1,0,0]
=> [3,1,5,2,6,4] => [3,3]
=> [3]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [6,1,4,2,3,5] => [4,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => [4,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => [3,2,1]
=> [2,1]
=> 1
[1,0,1,1,1,0,0,0,1,0]
=> [3,1,4,6,2,5] => [3,3]
=> [3]
=> 1
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => [3,2,1]
=> [2,1]
=> 1
[1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => [3,2,1]
=> [2,1]
=> 1
[1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => [4,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,0,1,0,1,0,1,0]
=> [2,6,1,3,4,5] => [4,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => [3,3]
=> [3]
=> 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => [3,3]
=> [3]
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,6,1,5,3,4] => [3,2,1]
=> [2,1]
=> 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => [4,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,0,0,1,0,1,0]
=> [6,3,1,2,4,5] => [4,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,0,0,1,1,0,0]
=> [5,3,1,2,6,4] => [3,2,1]
=> [2,1]
=> 1
[1,1,0,1,0,1,0,0,1,0]
=> [6,4,1,2,3,5] => [4,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,0,1,0,1,0,0]
=> [5,6,1,2,3,4] => [4,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,0,1,1,0,0,0]
=> [5,4,1,2,6,3] => [3,2,1]
=> [2,1]
=> 1
[1,1,0,1,1,0,0,0,1,0]
=> [4,3,1,6,2,5] => [3,2,1]
=> [2,1]
=> 1
[1,1,0,1,1,0,0,1,0,0]
=> [6,3,1,5,2,4] => [3,2,1]
=> [2,1]
=> 1
[1,1,0,1,1,0,1,0,0,0]
=> [6,4,1,5,2,3] => [3,2,1]
=> [2,1]
=> 1
[1,1,0,1,1,1,0,0,0,0]
=> [4,3,1,5,6,2] => [3,2,1]
=> [2,1]
=> 1
[1,1,1,0,0,0,1,0,1,0]
=> [2,3,6,1,4,5] => [4,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => [4,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,0,1,0,0,1,0]
=> [2,6,4,1,3,5] => [3,2,1]
=> [2,1]
=> 1
[1,1,1,0,0,1,0,1,0,0]
=> [2,6,5,1,3,4] => [3,2,1]
=> [2,1]
=> 1
[1,1,1,0,0,1,1,0,0,0]
=> [2,5,4,1,6,3] => [3,2,1]
=> [2,1]
=> 1
[1,1,1,0,1,0,0,0,1,0]
=> [6,3,4,1,2,5] => [3,2,1]
=> [2,1]
=> 1
[1,1,1,0,1,0,0,1,0,0]
=> [6,3,5,1,2,4] => [3,2,1]
=> [2,1]
=> 1
[1,1,1,0,1,0,1,0,0,0]
=> [6,5,4,1,2,3] => [3,1,1,1]
=> [1,1,1]
=> 1
[1,1,1,0,1,1,0,0,0,0]
=> [5,3,4,1,6,2] => [3,2,1]
=> [2,1]
=> 1
[1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => [4,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,1,0,0,0,1,0,0]
=> [2,3,6,5,1,4] => [3,2,1]
=> [2,1]
=> 1
[1,1,1,1,0,0,1,0,0,0]
=> [2,6,4,5,1,3] => [3,2,1]
=> [2,1]
=> 1
[1,1,1,1,0,1,0,0,0,0]
=> [6,3,4,5,1,2] => [3,2,1]
=> [2,1]
=> 1
[1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => [5,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [7,1,2,3,4,5,6] => [6,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [6,1,2,3,4,7,5] => [5,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,1,2,3,7,4,6] => [5,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [7,1,2,3,6,4,5] => [5,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [5,1,2,3,6,7,4] => [5,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [4,1,2,7,3,5,6] => [5,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,1,2,6,3,7,5] => [4,3]
=> [3]
=> 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [7,1,2,5,3,4,6] => [5,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [7,1,2,6,3,4,5] => [5,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [6,1,2,5,3,7,4] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [4,1,2,5,7,3,6] => [4,3]
=> [3]
=> 1
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [4,1,2,7,6,3,5] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [7,1,2,5,6,3,4] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [4,1,2,5,6,7,3] => [5,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [3,1,7,2,4,5,6] => [5,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [3,1,6,2,4,7,5] => [4,3]
=> [3]
=> 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [3,1,5,2,7,4,6] => [4,3]
=> [3]
=> 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [3,1,7,2,6,4,5] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,1,5,2,6,7,4] => [4,3]
=> [3]
=> 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [7,1,4,2,3,5,6] => [5,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [6,1,4,2,3,7,5] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [7,1,5,2,3,4,6] => [5,1,1]
=> [1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [6,1,7,2,3,4,5] => [5,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [6,1,5,2,3,7,4] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,1,4,2,7,3,6] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [7,1,4,2,6,3,5] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [7,1,5,2,6,3,4] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [5,1,4,2,6,7,3] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [3,1,4,7,2,5,6] => [4,3]
=> [3]
=> 1
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [3,1,4,6,2,7,5] => [4,3]
=> [3]
=> 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [3,1,7,5,2,4,6] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [3,1,7,6,2,4,5] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,1,6,5,2,7,4] => [3,3,1]
=> [3,1]
=> 1
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [7,1,4,5,2,3,6] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [7,1,4,6,2,3,5] => [4,2,1]
=> [2,1]
=> 1
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [7,1,6,5,2,3,4] => [4,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,1,4,5,6,7,2] => [5,2]
=> [2]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
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.
Mp00119: Dyck paths to 321-avoiding permutation (Krattenthaler)Permutations
Mp00108: Permutations cycle typeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001934: Integer partitions ⟶ ℤResult quality: 29% values known / values provided: 83%distinct values known / distinct values provided: 29%
Values
[1,0,1,0]
=> [1,2] => [1,1]
=> [1]
=> 1
[1,1,0,0]
=> [2,1] => [2]
=> []
=> ? = 2
[1,0,1,0,1,0]
=> [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,0]
=> [1,3,2] => [2,1]
=> [1]
=> 1
[1,1,0,0,1,0]
=> [2,1,3] => [2,1]
=> [1]
=> 1
[1,1,0,1,0,0]
=> [2,3,1] => [3]
=> []
=> ? ∊ {1,3}
[1,1,1,0,0,0]
=> [3,1,2] => [3]
=> []
=> ? ∊ {1,3}
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [2,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [2,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [3,1]
=> [1]
=> 1
[1,0,1,1,1,0,0,0]
=> [1,4,2,3] => [3,1]
=> [1]
=> 1
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,1]
=> [1,1]
=> 1
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,2]
=> [2]
=> 1
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => [3,1]
=> [1]
=> 1
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => [4]
=> []
=> ? ∊ {1,1,2,4}
[1,1,0,1,1,0,0,0]
=> [2,4,1,3] => [4]
=> []
=> ? ∊ {1,1,2,4}
[1,1,1,0,0,0,1,0]
=> [3,1,2,4] => [3,1]
=> [1]
=> 1
[1,1,1,0,0,1,0,0]
=> [3,1,4,2] => [4]
=> []
=> ? ∊ {1,1,2,4}
[1,1,1,0,1,0,0,0]
=> [3,4,1,2] => [2,2]
=> [2]
=> 1
[1,1,1,1,0,0,0,0]
=> [4,1,2,3] => [4]
=> []
=> ? ∊ {1,1,2,4}
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [3,1,1]
=> [1,1]
=> 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,3,4] => [3,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [2,2,1]
=> [2,1]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [3,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [4,1]
=> [1]
=> 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => [4,1]
=> [1]
=> 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,2,3,5] => [3,1,1]
=> [1,1]
=> 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,2,5,3] => [4,1]
=> [1]
=> 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,4,5,2,3] => [2,2,1]
=> [2,1]
=> 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,2,3,4] => [4,1]
=> [1]
=> 1
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,2,1]
=> [2,1]
=> 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,2,1]
=> [2,1]
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [3,2]
=> [2]
=> 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,3,4] => [3,2]
=> [2]
=> 1
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [3,1,1]
=> [1,1]
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [3,2]
=> [2]
=> 1
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [4,1]
=> [1]
=> 1
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [5]
=> []
=> ? ∊ {1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => [5]
=> []
=> ? ∊ {1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => [4,1]
=> [1]
=> 1
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,5,3] => [5]
=> []
=> ? ∊ {1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => [3,2]
=> [2]
=> 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,1,3,4] => [5]
=> []
=> ? ∊ {1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,2,4,5] => [3,1,1]
=> [1,1]
=> 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,1,2,5,4] => [3,2]
=> [2]
=> 1
[1,1,1,0,0,1,0,0,1,0]
=> [3,1,4,2,5] => [4,1]
=> [1]
=> 1
[1,1,1,0,0,1,0,1,0,0]
=> [3,1,4,5,2] => [5]
=> []
=> ? ∊ {1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,0,1,1,0,0,0]
=> [3,1,5,2,4] => [5]
=> []
=> ? ∊ {1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,1,0,0,0,1,0]
=> [3,4,1,2,5] => [2,2,1]
=> [2,1]
=> 1
[1,1,1,0,1,0,0,1,0,0]
=> [3,4,1,5,2] => [3,2]
=> [2]
=> 1
[1,1,1,0,1,0,1,0,0,0]
=> [3,4,5,1,2] => [5]
=> []
=> ? ∊ {1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,1,1,0,0,0,0]
=> [3,5,1,2,4] => [3,2]
=> [2]
=> 1
[1,1,1,1,0,0,0,0,1,0]
=> [4,1,2,3,5] => [4,1]
=> [1]
=> 1
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,5,3] => [5]
=> []
=> ? ∊ {1,1,1,2,2,2,2,2,2,5}
[1,1,1,1,0,0,1,0,0,0]
=> [4,1,5,2,3] => [3,2]
=> [2]
=> 1
[1,1,1,1,0,1,0,0,0,0]
=> [4,5,1,2,3] => [5]
=> []
=> ? ∊ {1,1,1,2,2,2,2,2,2,5}
[1,1,1,1,1,0,0,0,0,0]
=> [5,1,2,3,4] => [5]
=> []
=> ? ∊ {1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6] => [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,6,5] => [2,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,5,4,6] => [2,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,5,6,4] => [3,1,1,1]
=> [1,1,1]
=> 1
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,1] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [2,3,4,6,1,5] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,3,5,1,6,4] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,6,1,4,5] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,4,1,5,6,3] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [2,4,5,6,1,3] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,5,1,3,6,4] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,5,6,1,3,4] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,6,1,3,4,5] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [3,1,4,5,6,2] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,1,4,6,2,5] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [3,1,5,2,6,4] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,1,6,2,4,5] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [3,4,5,1,6,2] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [3,4,6,1,2,5] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [4,1,2,5,6,3] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [4,1,2,6,3,5] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [4,1,5,6,2,3] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [4,5,1,2,6,3] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [4,6,1,2,3,5] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,1,2,3,6,4] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [5,1,6,2,3,4] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [6,1,2,3,4,5] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,7,1] => [7]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [2,3,4,5,7,1,6] => [7]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [2,3,4,6,1,7,5] => [7]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,4,7,1,5,6] => [7]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [2,3,5,1,6,7,4] => [7]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [2,3,5,1,7,4,6] => [7]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [2,3,5,6,7,1,4] => [7]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
=> [2,3,6,1,4,7,5] => [7]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=> [2,3,6,7,1,4,5] => [7]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
Description
The number of monotone factorisations of genus zero of a permutation of given cycle type. A monotone factorisation of genus zero of a permutation $\pi\in\mathfrak S_n$ with $\ell$ cycles, including fixed points, is a tuple of $r = n - \ell$ transpositions $$ (a_1, b_1),\dots,(a_r, b_r) $$ with $b_1 \leq \dots \leq b_r$ and $a_i < b_i$ for all $i$, whose product, in this order, is $\pi$. For example, the cycle $(2,3,1)$ has the two factorizations $(2,3)(1,3)$ and $(1,2)(2,3)$.
Mp00024: Dyck paths to 321-avoiding permutationPermutations
Mp00065: Permutations permutation posetPosets
Mp00206: Posets antichains of maximal sizeLattices
St001878: Lattices ⟶ ℤResult quality: 29% values known / values provided: 75%distinct values known / distinct values provided: 29%
Values
[1,0,1,0]
=> [2,1] => ([],2)
=> ([],1)
=> ? ∊ {1,2}
[1,1,0,0]
=> [1,2] => ([(0,1)],2)
=> ([(0,1)],2)
=> ? ∊ {1,2}
[1,0,1,0,1,0]
=> [2,1,3] => ([(0,2),(1,2)],3)
=> ([],1)
=> ? ∊ {1,1,1,3}
[1,0,1,1,0,0]
=> [2,3,1] => ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,3}
[1,1,0,0,1,0]
=> [3,1,2] => ([(1,2)],3)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,3}
[1,1,0,1,0,0]
=> [1,3,2] => ([(0,1),(0,2)],3)
=> ([],1)
=> ? ∊ {1,1,1,3}
[1,1,1,0,0,0]
=> [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,0,1,0,1,0]
=> [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4}
[1,0,1,0,1,1,0,0]
=> [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,1,0,0,1,0]
=> [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,4}
[1,0,1,1,0,1,0,0]
=> [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4}
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,0,0,1,0,1,0]
=> [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,1,0,1,0,0,1,0]
=> [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4}
[1,1,0,1,0,1,0,0]
=> [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,4}
[1,1,0,1,1,0,0,0]
=> [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4}
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => ([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,1,0,0,1,0,0]
=> [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,4}
[1,1,1,0,1,0,0,0]
=> [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,4}
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,0,1,0,1,0,1,1,0,0]
=> [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [2,4,1,5,3] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,5,3,4] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,0,1,1,0,1,0,1,0,0]
=> [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => ([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,0,1,1,1,0,0,1,0,0]
=> [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,0,1,1,1,0,1,0,0,0]
=> [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,1,0,0,1,0,1,0,1,0]
=> [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,5,2,4] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [3,1,2,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,0,1,0,1,0,1,0,0]
=> [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,1,0,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,1,0,1,1,0,0,1,0,0]
=> [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,1,0,1,1,0,1,0,0,0]
=> [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,1,0,1,1,1,0,0,0,0]
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,1,0,0,0,1,0,1,0]
=> [4,1,5,2,3] => ([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[1,1,1,0,0,1,0,0,1,0]
=> [4,1,2,5,3] => ([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,2,5,3] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,1,1,0,1,0,0,0,1,0]
=> [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,1,0,1,0,0,1,0,0]
=> [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,1,1,0,1,0,1,0,0,0]
=> [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,1,1,0,1,1,0,0,0,0]
=> [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,1,1,1,0,0,0,1,0,0]
=> [1,5,2,3,4] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,1,1,0,0,1,0,0,0]
=> [1,2,5,3,4] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,1,1,1,0,1,0,0,0,0]
=> [1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,5}
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,1,4,3,6,5] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,4,1,3,6,5] => ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,1,4,6,3,5] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,4,1,6,3,5] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,4,6,1,3,5] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,3,5,6] => ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [2,4,1,3,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,1,4,5,3,6] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,4,1,5,3,6] => ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,4,5,1,3,6] => ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [2,1,4,5,6,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [2,4,1,5,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [2,4,5,1,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [2,1,5,3,6,4] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [2,1,3,5,4,6] => ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [2,1,3,4,6,5] => ([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,0,1,0,0,1,1,1,0,0,0]
=> [3,5,6,1,2,4] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,3,2,5,4,6] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,3,2,4,6,5] => ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,1,0,0,0,1,1,0,1,0,0]
=> [4,5,1,6,2,3] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,2,4,3,6,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,4,2,3,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([],1)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,2,3,5,6,4] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,6}
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
Mp00025: Dyck paths to 132-avoiding permutationPermutations
Mp00160: Permutations graph of inversionsGraphs
St000260: Graphs ⟶ ℤResult quality: 29% values known / values provided: 69%distinct values known / distinct values provided: 29%
Values
[1,0,1,0]
=> [2,1] => ([(0,1)],2)
=> 1
[1,1,0,0]
=> [1,2] => ([],2)
=> ? = 2
[1,0,1,0,1,0]
=> [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[1,0,1,1,0,0]
=> [2,3,1] => ([(0,2),(1,2)],3)
=> 1
[1,1,0,0,1,0]
=> [3,1,2] => ([(0,2),(1,2)],3)
=> 1
[1,1,0,1,0,0]
=> [2,1,3] => ([(1,2)],3)
=> ? ∊ {1,3}
[1,1,1,0,0,0]
=> [1,2,3] => ([],3)
=> ? ∊ {1,3}
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,4}
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,4}
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 1
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {1,1,1,1,4}
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {1,1,1,1,4}
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([],4)
=> ? ∊ {1,1,1,1,4}
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 1
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => ([(2,4),(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,1,1,0,1,0,0,0,0]
=> [2,1,3,4,5] => ([(3,4)],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([],5)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,2,2,5}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [5,4,3,6,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [4,5,3,2,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,4,2,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [4,3,5,2,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [3,4,5,2,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [5,4,2,3,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [4,5,2,3,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [5,3,2,4,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [4,3,2,5,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [3,4,2,5,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [5,2,3,4,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [4,2,3,5,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [5,4,3,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [4,5,3,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [5,3,4,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [4,3,5,1,2,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,4,5,1,2,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [5,4,2,1,3,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [4,5,2,1,3,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [5,3,2,1,4,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [4,3,2,1,5,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [3,4,2,1,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [5,2,3,1,4,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [4,2,3,1,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [3,2,4,1,5,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,6}
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Mp00100: Dyck paths touch compositionInteger compositions
Mp00040: Integer compositions to partitionInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St000781: Integer partitions ⟶ ℤResult quality: 14% values known / values provided: 69%distinct values known / distinct values provided: 14%
Values
[1,0,1,0]
=> [1,1] => [1,1]
=> [1]
=> 1
[1,1,0,0]
=> [2] => [2]
=> []
=> ? = 2
[1,0,1,0,1,0]
=> [1,1,1] => [1,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,0]
=> [1,2] => [2,1]
=> [1]
=> 1
[1,1,0,0,1,0]
=> [2,1] => [2,1]
=> [1]
=> 1
[1,1,0,1,0,0]
=> [3] => [3]
=> []
=> ? ∊ {1,3}
[1,1,1,0,0,0]
=> [3] => [3]
=> []
=> ? ∊ {1,3}
[1,0,1,0,1,0,1,0]
=> [1,1,1,1] => [1,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,0]
=> [1,1,2] => [2,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,0,1,0]
=> [1,2,1] => [2,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,1,0,0]
=> [1,3] => [3,1]
=> [1]
=> 1
[1,0,1,1,1,0,0,0]
=> [1,3] => [3,1]
=> [1]
=> 1
[1,1,0,0,1,0,1,0]
=> [2,1,1] => [2,1,1]
=> [1,1]
=> 1
[1,1,0,0,1,1,0,0]
=> [2,2] => [2,2]
=> [2]
=> 1
[1,1,0,1,0,0,1,0]
=> [3,1] => [3,1]
=> [1]
=> 1
[1,1,0,1,0,1,0,0]
=> [4] => [4]
=> []
=> ? ∊ {1,1,1,2,4}
[1,1,0,1,1,0,0,0]
=> [4] => [4]
=> []
=> ? ∊ {1,1,1,2,4}
[1,1,1,0,0,0,1,0]
=> [3,1] => [3,1]
=> [1]
=> 1
[1,1,1,0,0,1,0,0]
=> [4] => [4]
=> []
=> ? ∊ {1,1,1,2,4}
[1,1,1,0,1,0,0,0]
=> [4] => [4]
=> []
=> ? ∊ {1,1,1,2,4}
[1,1,1,1,0,0,0,0]
=> [4] => [4]
=> []
=> ? ∊ {1,1,1,2,4}
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1] => [1,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,2] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,2,1] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => [3,1,1]
=> [1,1]
=> 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => [3,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,2,1,1] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => [2,2,1]
=> [2,1]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,1] => [3,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,4] => [4,1]
=> [1]
=> 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,4] => [4,1]
=> [1]
=> 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,3,1] => [3,1,1]
=> [1,1]
=> 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,4] => [4,1]
=> [1]
=> 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,4] => [4,1]
=> [1]
=> 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,4] => [4,1]
=> [1]
=> 1
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,2] => [2,2,1]
=> [2,1]
=> 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => [2,2,1]
=> [2,1]
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,3] => [3,2]
=> [2]
=> 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,3] => [3,2]
=> [2]
=> 1
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,1] => [3,1,1]
=> [1,1]
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,2] => [3,2]
=> [2]
=> 1
[1,1,0,1,0,1,0,0,1,0]
=> [4,1] => [4,1]
=> [1]
=> 1
[1,1,0,1,0,1,0,1,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,0,1,1,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,1,0,0,0,1,0]
=> [4,1] => [4,1]
=> [1]
=> 1
[1,1,0,1,1,0,0,1,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,1,0,1,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,1,1,0,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,1] => [3,1,1]
=> [1,1]
=> 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,2] => [3,2]
=> [2]
=> 1
[1,1,1,0,0,1,0,0,1,0]
=> [4,1] => [4,1]
=> [1]
=> 1
[1,1,1,0,0,1,0,1,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,0,1,1,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,1,0,0,0,1,0]
=> [4,1] => [4,1]
=> [1]
=> 1
[1,1,1,0,1,0,0,1,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,1,0,1,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,1,1,0,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,1,0,0,0,0,1,0]
=> [4,1] => [4,1]
=> [1]
=> 1
[1,1,1,1,0,0,0,1,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,1,0,0,1,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,1,0,1,0,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,1,1,0,0,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1] => [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,2] => [2,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,2,1] => [2,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,3] => [3,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,3] => [3,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => [2,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => [2,2,1,1]
=> [2,1,1]
=> 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,3,1] => [3,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,4] => [4,1,1]
=> [1,1]
=> 1
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
Description
The number of proper colouring schemes of a Ferrers diagram. A colouring of a Ferrers diagram is proper if no two cells in a row or in a column have the same colour. The minimal number of colours needed is the maximum of the length and the first part of the partition, because we can restrict a latin square to the shape. We can associate to each colouring the integer partition recording how often each colour is used, see [1]. This statistic is the number of distinct such integer partitions that occur.
Mp00024: Dyck paths to 321-avoiding permutationPermutations
Mp00064: Permutations reversePermutations
Mp00127: Permutations left-to-right-maxima to Dyck pathDyck paths
St001199: Dyck paths ⟶ ℤResult quality: 14% values known / values provided: 69%distinct values known / distinct values provided: 14%
Values
[1,0,1,0]
=> [2,1] => [1,2] => [1,0,1,0]
=> 1
[1,1,0,0]
=> [1,2] => [2,1] => [1,1,0,0]
=> ? = 2
[1,0,1,0,1,0]
=> [2,1,3] => [3,1,2] => [1,1,1,0,0,0]
=> ? ∊ {1,3}
[1,0,1,1,0,0]
=> [2,3,1] => [1,3,2] => [1,0,1,1,0,0]
=> 1
[1,1,0,0,1,0]
=> [3,1,2] => [2,1,3] => [1,1,0,0,1,0]
=> 1
[1,1,0,1,0,0]
=> [1,3,2] => [2,3,1] => [1,1,0,1,0,0]
=> 1
[1,1,1,0,0,0]
=> [1,2,3] => [3,2,1] => [1,1,1,0,0,0]
=> ? ∊ {1,3}
[1,0,1,0,1,0,1,0]
=> [2,1,4,3] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> 1
[1,0,1,0,1,1,0,0]
=> [2,4,1,3] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
=> 1
[1,0,1,1,0,0,1,0]
=> [2,1,3,4] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,2,4}
[1,0,1,1,0,1,0,0]
=> [2,3,1,4] => [4,1,3,2] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,2,4}
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> 1
[1,1,0,0,1,0,1,0]
=> [3,1,4,2] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> 1
[1,1,0,1,0,0,1,0]
=> [3,1,2,4] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,2,4}
[1,1,0,1,0,1,0,0]
=> [1,3,2,4] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,2,4}
[1,1,0,1,1,0,0,0]
=> [1,3,4,2] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> 1
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> 1
[1,1,1,0,0,1,0,0]
=> [1,4,2,3] => [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> 1
[1,1,1,0,1,0,0,0]
=> [1,2,4,3] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
=> 1
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,2,4}
[1,0,1,0,1,0,1,0,1,0]
=> [2,1,4,3,5] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,0,1,1,0,0]
=> [2,4,1,3,5] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,1,0,0,1,0]
=> [2,1,4,5,3] => [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0]
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [2,4,1,5,3] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
=> 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,4,5,1,3] => [3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0]
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,5,3,4] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [2,5,1,3,4] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [2,1,3,5,4] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> 1
[1,0,1,1,0,1,0,1,0,0]
=> [2,3,1,5,4] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
=> 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0]
=> 1
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,4,5] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,1,1,0,0,1,0,0]
=> [2,3,1,4,5] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,1,1,0,1,0,0,0]
=> [2,3,4,1,5] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
=> 1
[1,1,0,0,1,0,1,0,1,0]
=> [3,1,4,2,5] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,0,1,0,1,1,0,0]
=> [3,4,1,2,5] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,0,1,1,0,0,1,0]
=> [3,1,4,5,2] => [2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0]
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [3,4,1,5,2] => [2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0]
=> 1
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> 1
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,5,2,4] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,5,1,2,4] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0]
=> 1
[1,1,0,1,0,1,0,0,1,0]
=> [3,1,2,5,4] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
=> 1
[1,1,0,1,0,1,0,1,0,0]
=> [1,3,2,5,4] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
=> 1
[1,1,0,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0]
=> 1
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,4,5] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,1,0,0,1,0,0]
=> [1,3,2,4,5] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,1,0,1,0,0,0]
=> [1,3,4,2,5] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,1,1,0,0,0,0]
=> [1,3,4,5,2] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
=> 1
[1,1,1,0,0,0,1,0,1,0]
=> [4,1,5,2,3] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0]
=> 1
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> 1
[1,1,1,0,0,1,0,0,1,0]
=> [4,1,2,5,3] => [3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0]
=> 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,2,5,3] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0]
=> 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,5,2,3] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
=> 1
[1,1,1,0,1,0,0,0,1,0]
=> [4,1,2,3,5] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,1,0,0,1,0,0]
=> [1,4,2,3,5] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,1,0,1,0,0,0]
=> [1,2,4,3,5] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,1,1,0,0,0,0]
=> [1,2,4,5,3] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0]
=> 1
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> 1
[1,1,1,1,0,0,0,1,0,0]
=> [1,5,2,3,4] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> 1
[1,1,1,1,0,0,1,0,0,0]
=> [1,2,5,3,4] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
=> 1
[1,1,1,1,0,1,0,0,0,0]
=> [1,2,3,5,4] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
=> 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,1,4,3,6,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,4,1,3,6,5] => [5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,1,4,6,3,5] => [5,3,6,4,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,4,1,6,3,5] => [5,3,6,1,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,4,6,1,3,5] => [5,3,1,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,3,5,6] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [2,4,1,3,5,6] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,1,4,5,3,6] => [6,3,5,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,4,1,5,3,6] => [6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,4,5,1,3,6] => [6,3,1,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [2,1,4,5,6,3] => [3,6,5,4,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [2,4,1,5,6,3] => [3,6,5,1,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [2,4,5,1,6,3] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,4,5,6,1,3] => [3,1,6,5,4,2] => [1,1,1,0,0,1,1,1,0,0,0,0]
=> 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [2,1,5,3,4,6] => [6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [2,5,1,3,4,6] => [6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [2,1,3,5,4,6] => [6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [2,3,1,5,4,6] => [6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4,6] => [6,4,1,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [2,1,3,4,5,6] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [2,3,1,4,5,6] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [2,3,4,1,5,6] => [6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,3,4,5,1,6] => [6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [3,1,4,2,5,6] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [3,4,1,2,5,6] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [3,1,4,5,2,6] => [6,2,5,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [3,4,1,5,2,6] => [6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,4,5,1,2,6] => [6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [3,1,5,2,4,6] => [6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,0,0,1,1,0,0]
=> [3,5,1,2,4,6] => [6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,0,1,0,0,1,0]
=> [3,1,2,5,4,6] => [6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,3,2,5,4,6] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,3,5,2,4,6] => [6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [3,1,2,4,5,6] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,3,2,4,5,6] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,3,4,2,5,6] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,3,4,5,2,6] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Mp00100: Dyck paths touch compositionInteger compositions
Mp00040: Integer compositions to partitionInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001901: Integer partitions ⟶ ℤResult quality: 14% values known / values provided: 69%distinct values known / distinct values provided: 14%
Values
[1,0,1,0]
=> [1,1] => [1,1]
=> [1]
=> 1
[1,1,0,0]
=> [2] => [2]
=> []
=> ? = 2
[1,0,1,0,1,0]
=> [1,1,1] => [1,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,0]
=> [1,2] => [2,1]
=> [1]
=> 1
[1,1,0,0,1,0]
=> [2,1] => [2,1]
=> [1]
=> 1
[1,1,0,1,0,0]
=> [3] => [3]
=> []
=> ? ∊ {1,3}
[1,1,1,0,0,0]
=> [3] => [3]
=> []
=> ? ∊ {1,3}
[1,0,1,0,1,0,1,0]
=> [1,1,1,1] => [1,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,0]
=> [1,1,2] => [2,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,0,1,0]
=> [1,2,1] => [2,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,1,0,0]
=> [1,3] => [3,1]
=> [1]
=> 1
[1,0,1,1,1,0,0,0]
=> [1,3] => [3,1]
=> [1]
=> 1
[1,1,0,0,1,0,1,0]
=> [2,1,1] => [2,1,1]
=> [1,1]
=> 1
[1,1,0,0,1,1,0,0]
=> [2,2] => [2,2]
=> [2]
=> 1
[1,1,0,1,0,0,1,0]
=> [3,1] => [3,1]
=> [1]
=> 1
[1,1,0,1,0,1,0,0]
=> [4] => [4]
=> []
=> ? ∊ {1,1,1,2,4}
[1,1,0,1,1,0,0,0]
=> [4] => [4]
=> []
=> ? ∊ {1,1,1,2,4}
[1,1,1,0,0,0,1,0]
=> [3,1] => [3,1]
=> [1]
=> 1
[1,1,1,0,0,1,0,0]
=> [4] => [4]
=> []
=> ? ∊ {1,1,1,2,4}
[1,1,1,0,1,0,0,0]
=> [4] => [4]
=> []
=> ? ∊ {1,1,1,2,4}
[1,1,1,1,0,0,0,0]
=> [4] => [4]
=> []
=> ? ∊ {1,1,1,2,4}
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1] => [1,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,2] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,2,1] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,3] => [3,1,1]
=> [1,1]
=> 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,3] => [3,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,2,1,1] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => [2,2,1]
=> [2,1]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,1] => [3,1,1]
=> [1,1]
=> 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,4] => [4,1]
=> [1]
=> 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,4] => [4,1]
=> [1]
=> 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,3,1] => [3,1,1]
=> [1,1]
=> 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,4] => [4,1]
=> [1]
=> 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,4] => [4,1]
=> [1]
=> 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,4] => [4,1]
=> [1]
=> 1
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,1,1] => [2,1,1,1]
=> [1,1,1]
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,2] => [2,2,1]
=> [2,1]
=> 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => [2,2,1]
=> [2,1]
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,3] => [3,2]
=> [2]
=> 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,3] => [3,2]
=> [2]
=> 1
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,1] => [3,1,1]
=> [1,1]
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,2] => [3,2]
=> [2]
=> 1
[1,1,0,1,0,1,0,0,1,0]
=> [4,1] => [4,1]
=> [1]
=> 1
[1,1,0,1,0,1,0,1,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,0,1,1,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,1,0,0,0,1,0]
=> [4,1] => [4,1]
=> [1]
=> 1
[1,1,0,1,1,0,0,1,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,1,0,1,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,1,1,0,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,1] => [3,1,1]
=> [1,1]
=> 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,2] => [3,2]
=> [2]
=> 1
[1,1,1,0,0,1,0,0,1,0]
=> [4,1] => [4,1]
=> [1]
=> 1
[1,1,1,0,0,1,0,1,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,0,1,1,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,1,0,0,0,1,0]
=> [4,1] => [4,1]
=> [1]
=> 1
[1,1,1,0,1,0,0,1,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,1,0,1,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,1,1,0,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,1,0,0,0,0,1,0]
=> [4,1] => [4,1]
=> [1]
=> 1
[1,1,1,1,0,0,0,1,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,1,0,0,1,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,1,0,1,0,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,1,1,0,0,0,0,0]
=> [5] => [5]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1] => [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,2] => [2,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,2,1] => [2,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,3] => [3,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,3] => [3,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => [2,1,1,1,1]
=> [1,1,1,1]
=> 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => [2,2,1,1]
=> [2,1,1]
=> 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,3,1] => [3,1,1,1]
=> [1,1,1]
=> 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,4] => [4,1,1]
=> [1,1]
=> 1
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,0,1,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,0,1,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [6] => [6]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
Description
The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition.
Mp00025: Dyck paths to 132-avoiding permutationPermutations
Mp00127: Permutations left-to-right-maxima to Dyck pathDyck paths
Mp00027: Dyck paths to partitionInteger partitions
St001933: Integer partitions ⟶ ℤResult quality: 14% values known / values provided: 68%distinct values known / distinct values provided: 14%
Values
[1,0,1,0]
=> [2,1] => [1,1,0,0]
=> []
=> ? = 2
[1,1,0,0]
=> [1,2] => [1,0,1,0]
=> [1]
=> 1
[1,0,1,0,1,0]
=> [3,2,1] => [1,1,1,0,0,0]
=> []
=> ? ∊ {1,3}
[1,0,1,1,0,0]
=> [2,3,1] => [1,1,0,1,0,0]
=> [1]
=> 1
[1,1,0,0,1,0]
=> [3,1,2] => [1,1,1,0,0,0]
=> []
=> ? ∊ {1,3}
[1,1,0,1,0,0]
=> [2,1,3] => [1,1,0,0,1,0]
=> [2]
=> 1
[1,1,1,0,0,0]
=> [1,2,3] => [1,0,1,0,1,0]
=> [2,1]
=> 1
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {1,1,1,2,4}
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [1,1,1,0,1,0,0,0]
=> [1]
=> 1
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {1,1,1,2,4}
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> [2]
=> 1
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [2,1]
=> 1
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {1,1,1,2,4}
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> [1]
=> 1
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {1,1,1,2,4}
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> [3]
=> 1
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [3,1]
=> 1
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,1,1,1,0,0,0,0]
=> []
=> ? ∊ {1,1,1,2,4}
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,1,1,0,0,0,1,0]
=> [3]
=> 1
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [3,2]
=> 1
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
=> [1]
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0]
=> [2]
=> 1
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0]
=> [2,1]
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
=> [1]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> [3]
=> 1
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0]
=> [3,1]
=> 1
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> [3]
=> 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> 1
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> [1]
=> 1
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> [2]
=> 1
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0]
=> [2,1]
=> 1
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
=> [1]
=> 1
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [4]
=> 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> 1
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [4]
=> 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> 1
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0]
=> [1]
=> 1
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> [4]
=> 1
[1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> 1
[1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> [4]
=> 1
[1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> 1
[1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> 1
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,5}
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> [4]
=> 1
[1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> 1
[1,1,1,1,0,1,0,0,0,0]
=> [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1]
=> 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0]
=> [2]
=> 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0]
=> [2,1]
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1]
=> 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> [3]
=> 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0]
=> [3,1]
=> 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0]
=> [3]
=> 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0]
=> [3,2]
=> 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0]
=> [3,2,1]
=> 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,0,1,1,0,0,0,1,0]
=> [6,3,4,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,0,0,1,0,1,0]
=> [6,5,2,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [6,4,2,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [6,3,2,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
Description
The largest multiplicity of a part in an integer partition.
Mp00027: Dyck paths to partitionInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
Mp00230: Integer partitions parallelogram polyominoDyck paths
St001493: Dyck paths ⟶ ℤResult quality: 29% values known / values provided: 63%distinct values known / distinct values provided: 29%
Values
[1,0,1,0]
=> [1]
=> []
=> []
=> ? ∊ {1,2}
[1,1,0,0]
=> []
=> ?
=> ?
=> ? ∊ {1,2}
[1,0,1,0,1,0]
=> [2,1]
=> [1]
=> [1,0]
=> 1
[1,0,1,1,0,0]
=> [1,1]
=> [1]
=> [1,0]
=> 1
[1,1,0,0,1,0]
=> [2]
=> []
=> []
=> ? ∊ {1,1,3}
[1,1,0,1,0,0]
=> [1]
=> []
=> []
=> ? ∊ {1,1,3}
[1,1,1,0,0,0]
=> []
=> ?
=> ?
=> ? ∊ {1,1,3}
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> 1
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> 1
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [1,1]
=> [1,1,0,0]
=> 1
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 1
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 1
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [2]
=> [1,0,1,0]
=> 1
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [2]
=> [1,0,1,0]
=> 1
[1,1,0,1,0,0,1,0]
=> [3,1]
=> [1]
=> [1,0]
=> 1
[1,1,0,1,0,1,0,0]
=> [2,1]
=> [1]
=> [1,0]
=> 1
[1,1,0,1,1,0,0,0]
=> [1,1]
=> [1]
=> [1,0]
=> 1
[1,1,1,0,0,0,1,0]
=> [3]
=> []
=> []
=> ? ∊ {1,1,2,4}
[1,1,1,0,0,1,0,0]
=> [2]
=> []
=> []
=> ? ∊ {1,1,2,4}
[1,1,1,0,1,0,0,0]
=> [1]
=> []
=> []
=> ? ∊ {1,1,2,4}
[1,1,1,1,0,0,0,0]
=> []
=> ?
=> ?
=> ? ∊ {1,1,2,4}
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 2
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> 1
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> 1
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> 1
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 1
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 1
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> 1
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> 1
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> 1
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> 1
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [1,1]
=> [1,1,0,0]
=> 1
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [1,1]
=> [1,1,0,0]
=> 1
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [1,1]
=> [1,1,0,0]
=> 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [1,1]
=> [1,1,0,0]
=> 1
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [3]
=> [1,0,1,0,1,0]
=> 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [3]
=> [1,0,1,0,1,0]
=> 1
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [2]
=> [1,0,1,0]
=> 1
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [2]
=> [1,0,1,0]
=> 1
[1,1,1,0,0,1,1,0,0,0]
=> [2,2]
=> [2]
=> [1,0,1,0]
=> 1
[1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> [1]
=> [1,0]
=> 1
[1,1,1,0,1,0,0,1,0,0]
=> [3,1]
=> [1]
=> [1,0]
=> 1
[1,1,1,0,1,0,1,0,0,0]
=> [2,1]
=> [1]
=> [1,0]
=> 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,1]
=> [1]
=> [1,0]
=> 1
[1,1,1,1,0,0,0,0,1,0]
=> [4]
=> []
=> []
=> ? ∊ {2,2,2,2,5}
[1,1,1,1,0,0,0,1,0,0]
=> [3]
=> []
=> []
=> ? ∊ {2,2,2,2,5}
[1,1,1,1,0,0,1,0,0,0]
=> [2]
=> []
=> []
=> ? ∊ {2,2,2,2,5}
[1,1,1,1,0,1,0,0,0,0]
=> [1]
=> []
=> []
=> ? ∊ {2,2,2,2,5}
[1,1,1,1,1,0,0,0,0,0]
=> []
=> ?
=> ?
=> ? ∊ {2,2,2,2,5}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> [4,3,2,1]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> [4,3,2,1]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> [3,3,2,1]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [4,2,2,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [4,2,2,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> [4,3,1,1]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [4,3,1,1]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,1]
=> [4,2,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [4,2,1,1]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,1,1]
=> [4,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [4,1,1,1]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [5]
=> []
=> []
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [4]
=> []
=> []
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [3]
=> []
=> []
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [2]
=> []
=> []
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1]
=> []
=> []
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,1,1,1,1,1,0,0,0,0,0,0]
=> []
=> ?
=> ?
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,6}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,2,1]
=> [5,4,3,2,1]
=> [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,2,1]
=> [5,4,3,2,1]
=> [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,2,1]
=> [4,4,3,2,1]
=> [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [5,4,4,3,2,1]
=> [4,4,3,2,1]
=> [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [4,4,4,3,2,1]
=> [4,4,3,2,1]
=> [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> [5,3,3,2,1]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> [5,3,3,2,1]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,2,1]
=> [4,3,3,2,1]
=> [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [5,4,3,3,2,1]
=> [4,3,3,2,1]
=> [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=> [4,4,3,3,2,1]
=> [4,3,3,2,1]
=> [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [6,3,3,3,2,1]
=> [3,3,3,2,1]
=> [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [5,3,3,3,2,1]
=> [3,3,3,2,1]
=> [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [4,3,3,3,2,1]
=> [3,3,3,2,1]
=> [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [3,3,3,3,2,1]
=> [3,3,3,2,1]
=> [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
=> [4,4,4,2,2,1]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> [5,3,2,2,1]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,7}
Description
The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra.
The following 113 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000706The product of the factorials of the multiplicities of an integer partition. St000053The number of valleys of the Dyck path. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000291The number of descents of a binary word. St000306The bounce count of a Dyck path. St000326The position of the first one in a binary word after appending a 1 at the end. St000390The number of runs of ones in a binary word. St000617The number of global maxima of a Dyck path. St000627The exponent of a binary word. St000628The balance of a binary word. St000655The length of the minimal rise of a Dyck path. St000675The number of centered multitunnels of a Dyck path. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000913The number of ways to refine the partition into singletons. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St000964Gives the dimension of Ext^g(D(A),A) of the corresponding LNakayama algebra, when g denotes the global dimension of that algebra. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001063Numbers of 3-torsionfree simple modules in the corresponding Nakayama algebra. St001064Number of simple modules in the corresponding Nakayama algebra that are 3-syzygy modules. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001188The number of simple modules $S$ with grade $\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra $A$ corresponding to the Dyck path. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001205The number of non-simple indecomposable projective-injective modules of the algebra $eAe$ in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001238The number of simple modules S such that the Auslander-Reiten translate of S is isomorphic to the Nakayama functor applied to the second syzygy of S. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001256Number of simple reflexive modules that are 2-stable reflexive. St001289The vector space dimension of the n-fold tensor product of D(A), where n is maximal such that this n-fold tensor product is nonzero. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001481The minimal height of a peak of a Dyck path. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001503The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001722The number of minimal chains with small intervals between a binary word and the top element. St001732The number of peaks visible from the left. St001786The number of total orderings of the north steps of a Dyck path such that steps after the k-th east step are not among the first k positions in the order. St001884The number of borders of a binary word. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001597The Frobenius rank of a skew partition. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001568The smallest positive integer that does not appear twice in the partition. St000667The greatest common divisor of the parts of the partition. St001571The Cartan determinant of the integer partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000640The rank of the largest boolean interval in a poset. St000914The sum of the values of the Möbius function of a poset. St000100The number of linear extensions of a poset. St000618The number of self-evacuating tableaux of given shape. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000934The 2-degree of an integer partition. St001128The exponens consonantiae of a partition. St001280The number of parts of an integer partition that are at least two. St001432The order dimension of the partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001564The value of the forgotten symmetric functions when all variables set to 1. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001780The order of promotion on the set of standard tableaux of given shape. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001890The maximum magnitude of the Möbius function of a poset. St001330The hat guessing number of a graph. St000456The monochromatic index of a connected graph. St001344The neighbouring number of a permutation. St001162The minimum jump of a permutation. St000570The Edelman-Greene number of a permutation. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St001043The depth of the leaf closest to the root in the binary unordered tree associated with the perfect matching. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$. St001130The number of two successive successions in a permutation. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001877Number of indecomposable injective modules with projective dimension 2. St000181The number of connected components of the Hasse diagram for the poset. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St000633The size of the automorphism group of a poset. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001820The size of the image of the pop stack sorting operator. St001846The number of elements which do not have a complement in the lattice. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000741The Colin de Verdière graph invariant. St000657The smallest part of an integer composition. St000900The minimal number of repetitions of a part in an integer composition. St001267The length of the Lyndon factorization of the binary word. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001437The flex of a binary word. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St001219Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive.