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Your data matches 8 different statistics following compositions of up to 3 maps.
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Matching statistic: St001879
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Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00069: Permutations —complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[3,+,1] => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[3,-,1] => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[4,+,+,1] => [4,2,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,-,+,1] => [4,2,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,+,-,1] => [4,2,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,-,-,1] => [4,2,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[4,3,2,1] => [4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[5,+,+,+,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,-,+,+,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,+,-,+,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,+,+,-,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,-,-,+,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,-,+,-,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,+,-,-,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,-,-,-,1] => [5,2,3,4,1] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 9
[5,+,4,3,1] => [5,2,4,3,1] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,-,4,3,1] => [5,2,4,3,1] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,3,2,+,1] => [5,3,2,4,1] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,3,2,-,1] => [5,3,2,4,1] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[5,3,4,2,1] => [5,3,4,2,1] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[5,4,2,3,1] => [5,4,2,3,1] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[5,4,+,2,1] => [5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[5,4,-,2,1] => [5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[6,+,+,+,+,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,-,+,+,+,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,+,-,+,+,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,+,+,-,+,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,+,+,+,-,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,-,-,+,+,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,-,+,-,+,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,-,+,+,-,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,+,-,-,+,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,+,-,+,-,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,+,+,-,-,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,-,-,-,+,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,-,-,+,-,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,-,+,-,-,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,+,-,-,-,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,-,-,-,-,1] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 16
[6,+,+,5,4,1] => [6,2,3,5,4,1] => [1,5,4,2,3,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[6,-,+,5,4,1] => [6,2,3,5,4,1] => [1,5,4,2,3,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[6,+,-,5,4,1] => [6,2,3,5,4,1] => [1,5,4,2,3,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[6,-,-,5,4,1] => [6,2,3,5,4,1] => [1,5,4,2,3,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[6,+,4,3,+,1] => [6,2,4,3,5,1] => [1,5,3,4,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[6,-,4,3,+,1] => [6,2,4,3,5,1] => [1,5,3,4,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[6,+,4,3,-,1] => [6,2,4,3,5,1] => [1,5,3,4,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[6,-,4,3,-,1] => [6,2,4,3,5,1] => [1,5,3,4,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> 12
[6,+,4,5,3,1] => [6,2,4,5,3,1] => [1,5,3,2,4,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 10
[6,-,4,5,3,1] => [6,2,4,5,3,1] => [1,5,3,2,4,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 10
[6,+,5,3,4,1] => [6,2,5,3,4,1] => [1,5,2,4,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Matching statistic: St001605
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 18%●distinct values known / distinct values provided: 9%
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 18%●distinct values known / distinct values provided: 9%
Values
[3,+,1] => [3,2,1] => [3]
=> []
=> ? = 2 - 14
[3,-,1] => [3,2,1] => [3]
=> []
=> ? = 2 - 14
[4,+,+,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? = 4 - 14
[4,-,+,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? = 4 - 14
[4,+,-,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? = 4 - 14
[4,-,-,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? = 4 - 14
[4,3,2,1] => [4,3,2,1] => [4]
=> []
=> ? = 3 - 14
[5,+,+,+,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 14
[5,-,+,+,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 14
[5,+,-,+,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 14
[5,+,+,-,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 14
[5,-,-,+,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 14
[5,-,+,-,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 14
[5,+,-,-,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 14
[5,-,-,-,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 14
[5,+,4,3,1] => [5,2,4,3,1] => [4,1]
=> [1]
=> ? = 6 - 14
[5,-,4,3,1] => [5,2,4,3,1] => [4,1]
=> [1]
=> ? = 6 - 14
[5,3,2,+,1] => [5,3,2,4,1] => [4,1]
=> [1]
=> ? = 6 - 14
[5,3,2,-,1] => [5,3,2,4,1] => [4,1]
=> [1]
=> ? = 6 - 14
[5,3,4,2,1] => [5,3,4,2,1] => [4,1]
=> [1]
=> ? = 5 - 14
[5,4,2,3,1] => [5,4,2,3,1] => [4,1]
=> [1]
=> ? = 5 - 14
[5,4,+,2,1] => [5,4,3,2,1] => [5]
=> []
=> ? = 4 - 14
[5,4,-,2,1] => [5,4,3,2,1] => [5]
=> []
=> ? = 4 - 14
[6,+,+,+,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,-,+,+,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,+,-,+,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,+,+,-,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,+,+,+,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,-,-,+,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,-,+,-,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,-,+,+,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,+,-,-,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,+,-,+,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,+,+,-,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,-,-,-,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,-,-,+,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,-,+,-,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,+,-,-,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,-,-,-,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 2 = 16 - 14
[6,+,+,5,4,1] => [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 14
[6,-,+,5,4,1] => [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 14
[6,+,-,5,4,1] => [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 14
[6,-,-,5,4,1] => [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 14
[6,+,4,3,+,1] => [6,2,4,3,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 14
[6,-,4,3,+,1] => [6,2,4,3,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 14
[6,+,4,3,-,1] => [6,2,4,3,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 14
[6,-,4,3,-,1] => [6,2,4,3,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 14
[6,+,4,5,3,1] => [6,2,4,5,3,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 14
[6,-,4,5,3,1] => [6,2,4,5,3,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 14
[6,+,5,3,4,1] => [6,2,5,3,4,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 14
[6,-,5,3,4,1] => [6,2,5,3,4,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 14
[6,+,5,+,3,1] => [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 8 - 14
[6,-,5,+,3,1] => [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 8 - 14
[6,+,5,-,3,1] => [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 8 - 14
[6,-,5,-,3,1] => [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 8 - 14
[6,3,2,+,+,1] => [6,3,2,4,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 14
[6,3,2,-,+,1] => [6,3,2,4,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 14
[6,3,2,+,-,1] => [6,3,2,4,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 14
[6,3,2,-,-,1] => [6,3,2,4,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 14
[6,3,2,5,4,1] => [6,3,2,5,4,1] => [4,2]
=> [2]
=> ? = 8 - 14
[6,3,4,2,+,1] => [6,3,4,2,5,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 14
[6,3,4,2,-,1] => [6,3,4,2,5,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 14
[6,3,4,5,2,1] => [6,3,4,5,2,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 14
[6,3,5,2,4,1] => [6,3,5,2,4,1] => [4,1,1]
=> [1,1]
=> ? = 7 - 14
[6,3,5,+,2,1] => [6,3,5,4,2,1] => [5,1]
=> [1]
=> ? = 7 - 14
[6,3,5,-,2,1] => [6,3,5,4,2,1] => [5,1]
=> [1]
=> ? = 7 - 14
Description
The number of colourings of a cycle such that the multiplicities of colours are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the cyclic group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001603
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 18%●distinct values known / distinct values provided: 9%
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 18%●distinct values known / distinct values provided: 9%
Values
[3,+,1] => [3,2,1] => [3]
=> []
=> ? = 2 - 15
[3,-,1] => [3,2,1] => [3]
=> []
=> ? = 2 - 15
[4,+,+,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? = 4 - 15
[4,-,+,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? = 4 - 15
[4,+,-,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? = 4 - 15
[4,-,-,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? = 4 - 15
[4,3,2,1] => [4,3,2,1] => [4]
=> []
=> ? = 3 - 15
[5,+,+,+,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 15
[5,-,+,+,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 15
[5,+,-,+,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 15
[5,+,+,-,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 15
[5,-,-,+,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 15
[5,-,+,-,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 15
[5,+,-,-,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 15
[5,-,-,-,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 15
[5,+,4,3,1] => [5,2,4,3,1] => [4,1]
=> [1]
=> ? = 6 - 15
[5,-,4,3,1] => [5,2,4,3,1] => [4,1]
=> [1]
=> ? = 6 - 15
[5,3,2,+,1] => [5,3,2,4,1] => [4,1]
=> [1]
=> ? = 6 - 15
[5,3,2,-,1] => [5,3,2,4,1] => [4,1]
=> [1]
=> ? = 6 - 15
[5,3,4,2,1] => [5,3,4,2,1] => [4,1]
=> [1]
=> ? = 5 - 15
[5,4,2,3,1] => [5,4,2,3,1] => [4,1]
=> [1]
=> ? = 5 - 15
[5,4,+,2,1] => [5,4,3,2,1] => [5]
=> []
=> ? = 4 - 15
[5,4,-,2,1] => [5,4,3,2,1] => [5]
=> []
=> ? = 4 - 15
[6,+,+,+,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,-,+,+,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,+,-,+,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,+,+,-,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,+,+,+,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,-,-,+,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,-,+,-,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,-,+,+,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,+,-,-,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,+,-,+,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,+,+,-,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,-,-,-,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,-,-,+,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,-,+,-,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,+,-,-,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,-,-,-,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 1 = 16 - 15
[6,+,+,5,4,1] => [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 15
[6,-,+,5,4,1] => [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 15
[6,+,-,5,4,1] => [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 15
[6,-,-,5,4,1] => [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 15
[6,+,4,3,+,1] => [6,2,4,3,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 15
[6,-,4,3,+,1] => [6,2,4,3,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 15
[6,+,4,3,-,1] => [6,2,4,3,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 15
[6,-,4,3,-,1] => [6,2,4,3,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 15
[6,+,4,5,3,1] => [6,2,4,5,3,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 15
[6,-,4,5,3,1] => [6,2,4,5,3,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 15
[6,+,5,3,4,1] => [6,2,5,3,4,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 15
[6,-,5,3,4,1] => [6,2,5,3,4,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 15
[6,+,5,+,3,1] => [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 8 - 15
[6,-,5,+,3,1] => [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 8 - 15
[6,+,5,-,3,1] => [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 8 - 15
[6,-,5,-,3,1] => [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 8 - 15
[6,3,2,+,+,1] => [6,3,2,4,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 15
[6,3,2,-,+,1] => [6,3,2,4,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 15
[6,3,2,+,-,1] => [6,3,2,4,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 15
[6,3,2,-,-,1] => [6,3,2,4,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 15
[6,3,2,5,4,1] => [6,3,2,5,4,1] => [4,2]
=> [2]
=> ? = 8 - 15
[6,3,4,2,+,1] => [6,3,4,2,5,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 15
[6,3,4,2,-,1] => [6,3,4,2,5,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 15
[6,3,4,5,2,1] => [6,3,4,5,2,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 15
[6,3,5,2,4,1] => [6,3,5,2,4,1] => [4,1,1]
=> [1,1]
=> ? = 7 - 15
[6,3,5,+,2,1] => [6,3,5,4,2,1] => [5,1]
=> [1]
=> ? = 7 - 15
[6,3,5,-,2,1] => [6,3,5,4,2,1] => [5,1]
=> [1]
=> ? = 7 - 15
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.
Matching statistic: St001604
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 18%●distinct values known / distinct values provided: 9%
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 9% ●values known / values provided: 18%●distinct values known / distinct values provided: 9%
Values
[3,+,1] => [3,2,1] => [3]
=> []
=> ? = 2 - 16
[3,-,1] => [3,2,1] => [3]
=> []
=> ? = 2 - 16
[4,+,+,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? = 4 - 16
[4,-,+,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? = 4 - 16
[4,+,-,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? = 4 - 16
[4,-,-,1] => [4,2,3,1] => [3,1]
=> [1]
=> ? = 4 - 16
[4,3,2,1] => [4,3,2,1] => [4]
=> []
=> ? = 3 - 16
[5,+,+,+,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 16
[5,-,+,+,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 16
[5,+,-,+,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 16
[5,+,+,-,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 16
[5,-,-,+,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 16
[5,-,+,-,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 16
[5,+,-,-,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 16
[5,-,-,-,1] => [5,2,3,4,1] => [3,1,1]
=> [1,1]
=> ? = 9 - 16
[5,+,4,3,1] => [5,2,4,3,1] => [4,1]
=> [1]
=> ? = 6 - 16
[5,-,4,3,1] => [5,2,4,3,1] => [4,1]
=> [1]
=> ? = 6 - 16
[5,3,2,+,1] => [5,3,2,4,1] => [4,1]
=> [1]
=> ? = 6 - 16
[5,3,2,-,1] => [5,3,2,4,1] => [4,1]
=> [1]
=> ? = 6 - 16
[5,3,4,2,1] => [5,3,4,2,1] => [4,1]
=> [1]
=> ? = 5 - 16
[5,4,2,3,1] => [5,4,2,3,1] => [4,1]
=> [1]
=> ? = 5 - 16
[5,4,+,2,1] => [5,4,3,2,1] => [5]
=> []
=> ? = 4 - 16
[5,4,-,2,1] => [5,4,3,2,1] => [5]
=> []
=> ? = 4 - 16
[6,+,+,+,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,-,+,+,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,+,-,+,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,+,+,-,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,+,+,+,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,-,-,+,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,-,+,-,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,-,+,+,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,+,-,-,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,+,-,+,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,+,+,-,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,-,-,-,+,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,-,-,+,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,-,+,-,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,+,-,-,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,-,-,-,-,1] => [6,2,3,4,5,1] => [3,1,1,1]
=> [1,1,1]
=> 0 = 16 - 16
[6,+,+,5,4,1] => [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 16
[6,-,+,5,4,1] => [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 16
[6,+,-,5,4,1] => [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 16
[6,-,-,5,4,1] => [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 16
[6,+,4,3,+,1] => [6,2,4,3,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 16
[6,-,4,3,+,1] => [6,2,4,3,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 16
[6,+,4,3,-,1] => [6,2,4,3,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 16
[6,-,4,3,-,1] => [6,2,4,3,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 16
[6,+,4,5,3,1] => [6,2,4,5,3,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 16
[6,-,4,5,3,1] => [6,2,4,5,3,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 16
[6,+,5,3,4,1] => [6,2,5,3,4,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 16
[6,-,5,3,4,1] => [6,2,5,3,4,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 16
[6,+,5,+,3,1] => [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 8 - 16
[6,-,5,+,3,1] => [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 8 - 16
[6,+,5,-,3,1] => [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 8 - 16
[6,-,5,-,3,1] => [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 8 - 16
[6,3,2,+,+,1] => [6,3,2,4,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 16
[6,3,2,-,+,1] => [6,3,2,4,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 16
[6,3,2,+,-,1] => [6,3,2,4,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 16
[6,3,2,-,-,1] => [6,3,2,4,5,1] => [4,1,1]
=> [1,1]
=> ? = 12 - 16
[6,3,2,5,4,1] => [6,3,2,5,4,1] => [4,2]
=> [2]
=> ? = 8 - 16
[6,3,4,2,+,1] => [6,3,4,2,5,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 16
[6,3,4,2,-,1] => [6,3,4,2,5,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 16
[6,3,4,5,2,1] => [6,3,4,5,2,1] => [4,1,1]
=> [1,1]
=> ? = 10 - 16
[6,3,5,2,4,1] => [6,3,5,2,4,1] => [4,1,1]
=> [1,1]
=> ? = 7 - 16
[6,3,5,+,2,1] => [6,3,5,4,2,1] => [5,1]
=> [1]
=> ? = 7 - 16
[6,3,5,-,2,1] => [6,3,5,4,2,1] => [5,1]
=> [1]
=> ? = 7 - 16
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons.
Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St000680
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000680: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 36%
Mp00209: Permutations —pattern poset⟶ Posets
St000680: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 36%
Values
[3,+,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[3,-,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[4,+,+,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5 = 4 + 1
[4,-,+,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5 = 4 + 1
[4,+,-,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5 = 4 + 1
[4,-,-,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5 = 4 + 1
[4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[5,+,+,+,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,-,+,+,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,+,-,+,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,+,+,-,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,-,-,+,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,-,+,-,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,+,-,-,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,-,-,-,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,+,4,3,1] => [5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 6 + 1
[5,-,4,3,1] => [5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 6 + 1
[5,3,2,+,1] => [5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 6 + 1
[5,3,2,-,1] => [5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 6 + 1
[5,3,4,2,1] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5 + 1
[5,4,2,3,1] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5 + 1
[5,4,+,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[5,4,-,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[6,+,+,+,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,+,+,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,-,+,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,+,-,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,+,+,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,-,+,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,+,-,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,+,+,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,-,-,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,-,+,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,+,-,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,-,-,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,-,+,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,+,-,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,-,-,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,-,-,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,+,5,4,1] => [6,2,3,5,4,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,-,+,5,4,1] => [6,2,3,5,4,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,+,-,5,4,1] => [6,2,3,5,4,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,-,-,5,4,1] => [6,2,3,5,4,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,+,4,3,+,1] => [6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(1,8),(1,18),(2,12),(2,13),(2,14),(2,18),(3,10),(3,11),(3,14),(3,18),(4,8),(4,9),(4,11),(4,13),(5,7),(5,9),(5,10),(5,12),(7,15),(7,19),(8,15),(8,20),(9,15),(9,16),(9,17),(10,16),(10,19),(10,23),(11,16),(11,20),(11,23),(12,17),(12,19),(12,23),(13,17),(13,20),(13,23),(14,23),(15,22),(16,21),(16,22),(17,21),(17,22),(18,19),(18,20),(18,23),(19,21),(19,22),(20,21),(20,22),(21,6),(22,6),(23,21)],24)
=> ? = 12 + 1
[6,-,4,3,+,1] => [6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(1,8),(1,18),(2,12),(2,13),(2,14),(2,18),(3,10),(3,11),(3,14),(3,18),(4,8),(4,9),(4,11),(4,13),(5,7),(5,9),(5,10),(5,12),(7,15),(7,19),(8,15),(8,20),(9,15),(9,16),(9,17),(10,16),(10,19),(10,23),(11,16),(11,20),(11,23),(12,17),(12,19),(12,23),(13,17),(13,20),(13,23),(14,23),(15,22),(16,21),(16,22),(17,21),(17,22),(18,19),(18,20),(18,23),(19,21),(19,22),(20,21),(20,22),(21,6),(22,6),(23,21)],24)
=> ? = 12 + 1
[6,+,4,3,-,1] => [6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(1,8),(1,18),(2,12),(2,13),(2,14),(2,18),(3,10),(3,11),(3,14),(3,18),(4,8),(4,9),(4,11),(4,13),(5,7),(5,9),(5,10),(5,12),(7,15),(7,19),(8,15),(8,20),(9,15),(9,16),(9,17),(10,16),(10,19),(10,23),(11,16),(11,20),(11,23),(12,17),(12,19),(12,23),(13,17),(13,20),(13,23),(14,23),(15,22),(16,21),(16,22),(17,21),(17,22),(18,19),(18,20),(18,23),(19,21),(19,22),(20,21),(20,22),(21,6),(22,6),(23,21)],24)
=> ? = 12 + 1
[6,-,4,3,-,1] => [6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(1,8),(1,18),(2,12),(2,13),(2,14),(2,18),(3,10),(3,11),(3,14),(3,18),(4,8),(4,9),(4,11),(4,13),(5,7),(5,9),(5,10),(5,12),(7,15),(7,19),(8,15),(8,20),(9,15),(9,16),(9,17),(10,16),(10,19),(10,23),(11,16),(11,20),(11,23),(12,17),(12,19),(12,23),(13,17),(13,20),(13,23),(14,23),(15,22),(16,21),(16,22),(17,21),(17,22),(18,19),(18,20),(18,23),(19,21),(19,22),(20,21),(20,22),(21,6),(22,6),(23,21)],24)
=> ? = 12 + 1
[6,+,4,5,3,1] => [6,2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,17),(2,10),(2,11),(2,17),(3,8),(3,9),(3,13),(3,17),(4,7),(4,9),(4,10),(4,17),(5,7),(5,8),(5,11),(5,12),(7,15),(7,20),(7,21),(8,14),(8,15),(8,20),(9,15),(9,16),(9,21),(10,21),(11,20),(11,21),(12,14),(12,20),(13,14),(13,16),(14,19),(15,18),(15,19),(16,18),(16,19),(17,16),(17,20),(17,21),(18,6),(19,6),(20,18),(20,19),(21,18)],22)
=> ? = 10 + 1
[6,-,4,5,3,1] => [6,2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,17),(2,10),(2,11),(2,17),(3,8),(3,9),(3,13),(3,17),(4,7),(4,9),(4,10),(4,17),(5,7),(5,8),(5,11),(5,12),(7,15),(7,20),(7,21),(8,14),(8,15),(8,20),(9,15),(9,16),(9,21),(10,21),(11,20),(11,21),(12,14),(12,20),(13,14),(13,16),(14,19),(15,18),(15,19),(16,18),(16,19),(17,16),(17,20),(17,21),(18,6),(19,6),(20,18),(20,19),(21,18)],22)
=> ? = 10 + 1
[6,+,5,3,4,1] => [6,2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,17),(2,10),(2,11),(2,17),(3,8),(3,9),(3,13),(3,17),(4,7),(4,9),(4,10),(4,17),(5,7),(5,8),(5,11),(5,12),(7,15),(7,20),(7,21),(8,14),(8,15),(8,20),(9,15),(9,16),(9,21),(10,21),(11,20),(11,21),(12,14),(12,20),(13,14),(13,16),(14,19),(15,18),(15,19),(16,18),(16,19),(17,16),(17,20),(17,21),(18,6),(19,6),(20,18),(20,19),(21,18)],22)
=> ? = 10 + 1
[6,-,5,3,4,1] => [6,2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,17),(2,10),(2,11),(2,17),(3,8),(3,9),(3,13),(3,17),(4,7),(4,9),(4,10),(4,17),(5,7),(5,8),(5,11),(5,12),(7,15),(7,20),(7,21),(8,14),(8,15),(8,20),(9,15),(9,16),(9,21),(10,21),(11,20),(11,21),(12,14),(12,20),(13,14),(13,16),(14,19),(15,18),(15,19),(16,18),(16,19),(17,16),(17,20),(17,21),(18,6),(19,6),(20,18),(20,19),(21,18)],22)
=> ? = 10 + 1
[6,+,5,+,3,1] => [6,2,5,4,3,1] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 8 + 1
[6,-,5,+,3,1] => [6,2,5,4,3,1] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 8 + 1
[6,+,5,-,3,1] => [6,2,5,4,3,1] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 8 + 1
[6,-,5,-,3,1] => [6,2,5,4,3,1] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 8 + 1
[6,3,2,+,+,1] => [6,3,2,4,5,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,3,2,-,+,1] => [6,3,2,4,5,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,3,2,+,-,1] => [6,3,2,4,5,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,3,2,-,-,1] => [6,3,2,4,5,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,5,4,3,2,1] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
Description
The Grundy value for Hackendot on posets.
Two players take turns and remove an order filter. The player who is faced with the one element poset looses. This game is a slight variation of Chomp.
This statistic is the Grundy value of the poset, that is, the smallest non-negative integer which does not occur as value of a poset obtained by a single move.
Matching statistic: St000912
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000912: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 36%
Mp00209: Permutations —pattern poset⟶ Posets
St000912: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 36%
Values
[3,+,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[3,-,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 3 = 2 + 1
[4,+,+,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5 = 4 + 1
[4,-,+,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5 = 4 + 1
[4,+,-,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5 = 4 + 1
[4,-,-,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 5 = 4 + 1
[4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[5,+,+,+,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,-,+,+,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,+,-,+,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,+,+,-,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,-,-,+,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,-,+,-,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,+,-,-,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,-,-,-,1] => [5,2,3,4,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 9 + 1
[5,+,4,3,1] => [5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 6 + 1
[5,-,4,3,1] => [5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 6 + 1
[5,3,2,+,1] => [5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 6 + 1
[5,3,2,-,1] => [5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 6 + 1
[5,3,4,2,1] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5 + 1
[5,4,2,3,1] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 5 + 1
[5,4,+,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[5,4,-,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[6,+,+,+,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,+,+,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,-,+,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,+,-,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,+,+,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,-,+,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,+,-,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,+,+,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,-,-,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,-,+,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,+,-,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,-,-,+,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,-,+,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,+,-,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,-,-,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,-,-,-,-,1] => [6,2,3,4,5,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
=> ? = 16 + 1
[6,+,+,5,4,1] => [6,2,3,5,4,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,-,+,5,4,1] => [6,2,3,5,4,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,+,-,5,4,1] => [6,2,3,5,4,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,-,-,5,4,1] => [6,2,3,5,4,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,+,4,3,+,1] => [6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(1,8),(1,18),(2,12),(2,13),(2,14),(2,18),(3,10),(3,11),(3,14),(3,18),(4,8),(4,9),(4,11),(4,13),(5,7),(5,9),(5,10),(5,12),(7,15),(7,19),(8,15),(8,20),(9,15),(9,16),(9,17),(10,16),(10,19),(10,23),(11,16),(11,20),(11,23),(12,17),(12,19),(12,23),(13,17),(13,20),(13,23),(14,23),(15,22),(16,21),(16,22),(17,21),(17,22),(18,19),(18,20),(18,23),(19,21),(19,22),(20,21),(20,22),(21,6),(22,6),(23,21)],24)
=> ? = 12 + 1
[6,-,4,3,+,1] => [6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(1,8),(1,18),(2,12),(2,13),(2,14),(2,18),(3,10),(3,11),(3,14),(3,18),(4,8),(4,9),(4,11),(4,13),(5,7),(5,9),(5,10),(5,12),(7,15),(7,19),(8,15),(8,20),(9,15),(9,16),(9,17),(10,16),(10,19),(10,23),(11,16),(11,20),(11,23),(12,17),(12,19),(12,23),(13,17),(13,20),(13,23),(14,23),(15,22),(16,21),(16,22),(17,21),(17,22),(18,19),(18,20),(18,23),(19,21),(19,22),(20,21),(20,22),(21,6),(22,6),(23,21)],24)
=> ? = 12 + 1
[6,+,4,3,-,1] => [6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(1,8),(1,18),(2,12),(2,13),(2,14),(2,18),(3,10),(3,11),(3,14),(3,18),(4,8),(4,9),(4,11),(4,13),(5,7),(5,9),(5,10),(5,12),(7,15),(7,19),(8,15),(8,20),(9,15),(9,16),(9,17),(10,16),(10,19),(10,23),(11,16),(11,20),(11,23),(12,17),(12,19),(12,23),(13,17),(13,20),(13,23),(14,23),(15,22),(16,21),(16,22),(17,21),(17,22),(18,19),(18,20),(18,23),(19,21),(19,22),(20,21),(20,22),(21,6),(22,6),(23,21)],24)
=> ? = 12 + 1
[6,-,4,3,-,1] => [6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(1,8),(1,18),(2,12),(2,13),(2,14),(2,18),(3,10),(3,11),(3,14),(3,18),(4,8),(4,9),(4,11),(4,13),(5,7),(5,9),(5,10),(5,12),(7,15),(7,19),(8,15),(8,20),(9,15),(9,16),(9,17),(10,16),(10,19),(10,23),(11,16),(11,20),(11,23),(12,17),(12,19),(12,23),(13,17),(13,20),(13,23),(14,23),(15,22),(16,21),(16,22),(17,21),(17,22),(18,19),(18,20),(18,23),(19,21),(19,22),(20,21),(20,22),(21,6),(22,6),(23,21)],24)
=> ? = 12 + 1
[6,+,4,5,3,1] => [6,2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,17),(2,10),(2,11),(2,17),(3,8),(3,9),(3,13),(3,17),(4,7),(4,9),(4,10),(4,17),(5,7),(5,8),(5,11),(5,12),(7,15),(7,20),(7,21),(8,14),(8,15),(8,20),(9,15),(9,16),(9,21),(10,21),(11,20),(11,21),(12,14),(12,20),(13,14),(13,16),(14,19),(15,18),(15,19),(16,18),(16,19),(17,16),(17,20),(17,21),(18,6),(19,6),(20,18),(20,19),(21,18)],22)
=> ? = 10 + 1
[6,-,4,5,3,1] => [6,2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,17),(2,10),(2,11),(2,17),(3,8),(3,9),(3,13),(3,17),(4,7),(4,9),(4,10),(4,17),(5,7),(5,8),(5,11),(5,12),(7,15),(7,20),(7,21),(8,14),(8,15),(8,20),(9,15),(9,16),(9,21),(10,21),(11,20),(11,21),(12,14),(12,20),(13,14),(13,16),(14,19),(15,18),(15,19),(16,18),(16,19),(17,16),(17,20),(17,21),(18,6),(19,6),(20,18),(20,19),(21,18)],22)
=> ? = 10 + 1
[6,+,5,3,4,1] => [6,2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,17),(2,10),(2,11),(2,17),(3,8),(3,9),(3,13),(3,17),(4,7),(4,9),(4,10),(4,17),(5,7),(5,8),(5,11),(5,12),(7,15),(7,20),(7,21),(8,14),(8,15),(8,20),(9,15),(9,16),(9,21),(10,21),(11,20),(11,21),(12,14),(12,20),(13,14),(13,16),(14,19),(15,18),(15,19),(16,18),(16,19),(17,16),(17,20),(17,21),(18,6),(19,6),(20,18),(20,19),(21,18)],22)
=> ? = 10 + 1
[6,-,5,3,4,1] => [6,2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,17),(2,10),(2,11),(2,17),(3,8),(3,9),(3,13),(3,17),(4,7),(4,9),(4,10),(4,17),(5,7),(5,8),(5,11),(5,12),(7,15),(7,20),(7,21),(8,14),(8,15),(8,20),(9,15),(9,16),(9,21),(10,21),(11,20),(11,21),(12,14),(12,20),(13,14),(13,16),(14,19),(15,18),(15,19),(16,18),(16,19),(17,16),(17,20),(17,21),(18,6),(19,6),(20,18),(20,19),(21,18)],22)
=> ? = 10 + 1
[6,+,5,+,3,1] => [6,2,5,4,3,1] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 8 + 1
[6,-,5,+,3,1] => [6,2,5,4,3,1] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 8 + 1
[6,+,5,-,3,1] => [6,2,5,4,3,1] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 8 + 1
[6,-,5,-,3,1] => [6,2,5,4,3,1] => ([(0,1),(0,3),(0,4),(0,5),(1,14),(2,7),(2,8),(2,16),(3,9),(3,11),(3,14),(4,9),(4,10),(4,14),(5,2),(5,10),(5,11),(5,14),(7,13),(7,15),(8,13),(8,15),(9,12),(9,16),(10,7),(10,12),(10,16),(11,8),(11,12),(11,16),(12,13),(12,15),(13,6),(14,16),(15,6),(16,15)],17)
=> ? = 8 + 1
[6,3,2,+,+,1] => [6,3,2,4,5,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,3,2,-,+,1] => [6,3,2,4,5,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,3,2,+,-,1] => [6,3,2,4,5,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,3,2,-,-,1] => [6,3,2,4,5,1] => ([(0,2),(0,3),(0,4),(0,5),(1,17),(2,8),(2,9),(2,12),(3,7),(3,9),(3,11),(4,7),(4,8),(4,10),(5,1),(5,10),(5,11),(5,12),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(10,17),(11,15),(11,16),(11,17),(12,14),(12,15),(12,17),(13,19),(14,18),(14,19),(15,18),(15,19),(16,18),(16,19),(17,18),(18,6),(19,6)],20)
=> ? = 12 + 1
[6,5,4,3,2,1] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 5 + 1
Description
The number of maximal antichains in a poset.
Matching statistic: St000422
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000422: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 9%
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000422: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 9%
Values
[3,+,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 2 - 5
[3,-,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 2 - 5
[4,+,+,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 4 - 5
[4,-,+,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 4 - 5
[4,+,-,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 4 - 5
[4,-,-,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 4 - 5
[4,3,2,1] => [4,3,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 3 - 5
[5,+,+,+,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 4 = 9 - 5
[5,-,+,+,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 4 = 9 - 5
[5,+,-,+,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 4 = 9 - 5
[5,+,+,-,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 4 = 9 - 5
[5,-,-,+,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 4 = 9 - 5
[5,-,+,-,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 4 = 9 - 5
[5,+,-,-,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 4 = 9 - 5
[5,-,-,-,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 4 = 9 - 5
[5,+,4,3,1] => [5,2,4,3,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 6 - 5
[5,-,4,3,1] => [5,2,4,3,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 6 - 5
[5,3,2,+,1] => [5,3,2,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 6 - 5
[5,3,2,-,1] => [5,3,2,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 6 - 5
[5,3,4,2,1] => [5,3,4,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 5
[5,4,2,3,1] => [5,4,2,3,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 5
[5,4,+,2,1] => [5,4,3,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 5
[5,4,-,2,1] => [5,4,3,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 5
[6,+,+,+,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,-,+,+,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,+,-,+,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,+,+,-,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,+,+,+,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,-,-,+,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,-,+,-,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,-,+,+,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,+,-,-,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,+,-,+,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,+,+,-,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,-,-,-,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,-,-,+,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,-,+,-,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,+,-,-,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,-,-,-,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 5
[6,+,+,5,4,1] => [6,2,3,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 5
[6,-,+,5,4,1] => [6,2,3,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 5
[6,+,-,5,4,1] => [6,2,3,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 5
[6,-,-,5,4,1] => [6,2,3,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 5
[6,+,4,3,+,1] => [6,2,4,3,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 5
[6,-,4,3,+,1] => [6,2,4,3,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 5
[6,+,4,3,-,1] => [6,2,4,3,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 5
[6,-,4,3,-,1] => [6,2,4,3,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 5
[6,+,4,5,3,1] => [6,2,4,5,3,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 10 - 5
[6,-,4,5,3,1] => [6,2,4,5,3,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 10 - 5
[6,+,5,3,4,1] => [6,2,5,3,4,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 10 - 5
[6,-,5,3,4,1] => [6,2,5,3,4,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 10 - 5
[6,+,5,+,3,1] => [6,2,5,4,3,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 8 - 5
[6,-,5,+,3,1] => [6,2,5,4,3,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 8 - 5
[6,+,5,-,3,1] => [6,2,5,4,3,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 8 - 5
[6,-,5,-,3,1] => [6,2,5,4,3,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 8 - 5
[6,3,2,+,+,1] => [6,3,2,4,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 5
[6,3,2,-,+,1] => [6,3,2,4,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 5
[6,3,2,+,-,1] => [6,3,2,4,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 5
Description
The energy of a graph, if it is integral.
The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3].
The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph Kn equals 2n−2. For this reason, we do not define the energy of the empty graph.
Matching statistic: St000454
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 9%
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 9%
Values
[3,+,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 2 - 7
[3,-,1] => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 2 - 7
[4,+,+,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 4 - 7
[4,-,+,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 4 - 7
[4,+,-,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 4 - 7
[4,-,-,1] => [4,2,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 4 - 7
[4,3,2,1] => [4,3,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 3 - 7
[5,+,+,+,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 9 - 7
[5,-,+,+,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 9 - 7
[5,+,-,+,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 9 - 7
[5,+,+,-,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 9 - 7
[5,-,-,+,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 9 - 7
[5,-,+,-,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 9 - 7
[5,+,-,-,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 9 - 7
[5,-,-,-,1] => [5,2,3,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 9 - 7
[5,+,4,3,1] => [5,2,4,3,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 6 - 7
[5,-,4,3,1] => [5,2,4,3,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 6 - 7
[5,3,2,+,1] => [5,3,2,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 6 - 7
[5,3,2,-,1] => [5,3,2,4,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 6 - 7
[5,3,4,2,1] => [5,3,4,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 7
[5,4,2,3,1] => [5,4,2,3,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 7
[5,4,+,2,1] => [5,4,3,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 7
[5,4,-,2,1] => [5,4,3,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 7
[6,+,+,+,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,-,+,+,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,+,-,+,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,+,+,-,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,+,+,+,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,-,-,+,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,-,+,-,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,-,+,+,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,+,-,-,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,+,-,+,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,+,+,-,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,-,-,-,+,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,-,-,+,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,-,+,-,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,+,-,-,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,-,-,-,-,1] => [6,2,3,4,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 16 - 7
[6,+,+,5,4,1] => [6,2,3,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 7
[6,-,+,5,4,1] => [6,2,3,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 7
[6,+,-,5,4,1] => [6,2,3,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 7
[6,-,-,5,4,1] => [6,2,3,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 7
[6,+,4,3,+,1] => [6,2,4,3,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 7
[6,-,4,3,+,1] => [6,2,4,3,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 7
[6,+,4,3,-,1] => [6,2,4,3,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 7
[6,-,4,3,-,1] => [6,2,4,3,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 7
[6,+,4,5,3,1] => [6,2,4,5,3,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 10 - 7
[6,-,4,5,3,1] => [6,2,4,5,3,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 10 - 7
[6,+,5,3,4,1] => [6,2,5,3,4,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 10 - 7
[6,-,5,3,4,1] => [6,2,5,3,4,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 10 - 7
[6,+,5,+,3,1] => [6,2,5,4,3,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 8 - 7
[6,-,5,+,3,1] => [6,2,5,4,3,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 8 - 7
[6,+,5,-,3,1] => [6,2,5,4,3,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 8 - 7
[6,-,5,-,3,1] => [6,2,5,4,3,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 8 - 7
[6,3,2,+,+,1] => [6,3,2,4,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 7
[6,3,2,-,+,1] => [6,3,2,4,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 7
[6,3,2,+,-,1] => [6,3,2,4,5,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 12 - 7
Description
The largest eigenvalue of a graph if it is integral.
If a graph is d-regular, then its largest eigenvalue equals d. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
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