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Your data matches 14 different statistics following compositions of up to 3 maps.
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(click to perform a complete search on your data)
Matching statistic: St000993
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[1,2,-3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[1,-2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[1,-2,-3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[-1,2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[-1,2,-3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[-1,-2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[-1,-2,-3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 2
[1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[1,2,3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[1,2,-3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[1,2,-3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[1,-2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[1,-2,3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[1,-2,-3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[1,-2,-3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[-1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[-1,2,3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[-1,2,-3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[-1,2,-3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[-1,-2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[-1,-2,3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[-1,-2,-3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[-1,-2,-3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 3
[1,2,4,3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,2,4,-3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,2,-4,3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,2,-4,-3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,-2,4,3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,-2,4,-3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,-2,-4,3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,-2,-4,-3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[-1,2,4,3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[-1,2,4,-3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[-1,2,-4,3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[-1,2,-4,-3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[-1,-2,4,3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[-1,-2,4,-3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[-1,-2,-4,3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[-1,-2,-4,-3] => [1,2,4,3] => [2,1,1]
=> [1,1]
=> 2
[1,3,2,4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[1,3,2,-4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[1,3,-2,4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[1,3,-2,-4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[1,-3,2,4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[1,-3,2,-4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[1,-3,-2,4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[1,-3,-2,-4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[-1,3,2,4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
[-1,3,2,-4] => [1,3,2,4] => [2,1,1]
=> [1,1]
=> 2
Description
The multiplicity of the largest part of an integer partition.
Matching statistic: St001935
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St001935: Parking functions ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Mp00305: Permutations —parking function⟶ Parking functions
St001935: Parking functions ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Values
[1,2,3] => [1,2,3] => [1,2,3] => 2
[1,2,-3] => [1,2,3] => [1,2,3] => 2
[1,-2,3] => [1,2,3] => [1,2,3] => 2
[1,-2,-3] => [1,2,3] => [1,2,3] => 2
[-1,2,3] => [1,2,3] => [1,2,3] => 2
[-1,2,-3] => [1,2,3] => [1,2,3] => 2
[-1,-2,3] => [1,2,3] => [1,2,3] => 2
[-1,-2,-3] => [1,2,3] => [1,2,3] => 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 3
[1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => 3
[1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => 3
[1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => 3
[1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => 3
[1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => 3
[1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => 3
[1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => 3
[-1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 3
[-1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => 3
[-1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => 3
[-1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => 3
[-1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => 3
[-1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => 3
[-1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => 3
[-1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => 3
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 2
[1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => 2
[1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => 2
[1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => 2
[1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => 2
[1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => 2
[1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => 2
[1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => 2
[-1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 2
[-1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => 2
[-1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => 2
[-1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => 2
[-1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => 2
[-1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => 2
[-1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => 2
[-1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => 2
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 2
[1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => 2
[1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => 2
[1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => 2
[1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => 2
[1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => 2
[1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => 2
[1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => 2
[-1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 2
[-1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => 2
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,2,3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,2,3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,2,3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,2,-3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,2,-3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,2,-3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,2,-3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,-2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,-2,3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,-2,3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,-2,3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,-2,-3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,-2,-3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,-2,-3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,-2,-3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,2,3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,2,3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,2,3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,2,-3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,2,-3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,2,-3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,2,-3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,-2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,-2,3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,-2,3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,-2,3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,-2,-3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,-2,-3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,-2,-3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[-1,-2,-3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,2,3,5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,2,3,-5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,2,3,-5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,2,-3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,2,-3,5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,2,-3,-5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,2,-3,-5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,-2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,-2,3,5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,-2,3,-5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,-2,3,-5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,-2,-3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,-2,-3,5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,-2,-3,-5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[1,-2,-3,-5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[-1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
[-1,2,3,5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 3
Description
The number of ascents in a parking function.
This is the number of indices $i$ such that $p_i > p_{i+1}$.
Matching statistic: St001946
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St001946: Parking functions ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Mp00069: Permutations —complement⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St001946: Parking functions ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Values
[1,2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 2
[1,2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 2
[1,-2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 2
[1,-2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 2
[-1,2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 2
[-1,2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 2
[-1,-2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 2
[-1,-2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 2
[1,2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[1,2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[1,2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[1,2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[1,-2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[1,-2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[1,-2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[1,-2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[-1,2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[-1,2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[-1,2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[-1,2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[-1,-2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[-1,-2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[-1,-2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[-1,-2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 3
[1,2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[1,2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[1,2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[1,2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[1,-2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[1,-2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[1,-2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[1,-2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[-1,2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[-1,2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[-1,2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[-1,2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[-1,-2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[-1,-2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[-1,-2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[-1,-2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 2
[1,3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 2
[1,3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 2
[1,3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 2
[1,3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 2
[1,-3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 2
[1,-3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 2
[1,-3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 2
[1,-3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 2
[-1,3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 2
[-1,3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 2
[1,2,3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,2,3,4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,2,3,-4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,2,3,-4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,2,-3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,2,-3,4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,2,-3,-4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,2,-3,-4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,-2,3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,-2,3,4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,-2,3,-4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,-2,3,-4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,-2,-3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,-2,-3,4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,-2,-3,-4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,-2,-3,-4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,2,3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,2,3,4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,2,3,-4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,2,3,-4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,2,-3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,2,-3,4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,2,-3,-4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,2,-3,-4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,-2,3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,-2,3,4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,-2,3,-4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,-2,3,-4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,-2,-3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,-2,-3,4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,-2,-3,-4,5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[-1,-2,-3,-4,-5] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 4
[1,2,3,5,4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,2,3,5,-4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,2,3,-5,4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,2,3,-5,-4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,2,-3,5,4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,2,-3,5,-4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,2,-3,-5,4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,2,-3,-5,-4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,-2,3,5,4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,-2,3,5,-4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,-2,3,-5,4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,-2,3,-5,-4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,-2,-3,5,4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,-2,-3,5,-4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,-2,-3,-5,4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,-2,-3,-5,-4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[-1,2,3,5,4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[-1,2,3,5,-4] => [1,2,3,5,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
Description
The number of descents in a parking function.
This is the number of indices $i$ such that $p_i > p_{i+1}$.
Matching statistic: St001773
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00329: Permutations —Tanimoto⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001773: Signed permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Mp00329: Permutations —Tanimoto⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001773: Signed permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Values
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 2 + 1
[1,2,-3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 2 + 1
[1,-2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 2 + 1
[1,-2,-3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 2 + 1
[-1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 2 + 1
[-1,2,-3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 2 + 1
[-1,-2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 2 + 1
[-1,-2,-3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 2 + 1
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[-1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[-1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[-1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[-1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[-1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[-1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[-1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[-1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 3 + 1
[1,2,4,3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[1,2,4,-3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[1,2,-4,3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[1,2,-4,-3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[1,-2,4,3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[1,-2,4,-3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[1,-2,-4,3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[1,-2,-4,-3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[-1,2,4,3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[-1,2,4,-3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[-1,2,-4,3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[-1,2,-4,-3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[-1,-2,4,3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[-1,-2,4,-3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[-1,-2,-4,3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[-1,-2,-4,-3] => [1,2,4,3] => [2,3,1,4] => [2,3,1,4] => 3 = 2 + 1
[1,3,2,4] => [1,3,2,4] => [1,2,4,3] => [1,2,4,3] => 3 = 2 + 1
[1,3,2,-4] => [1,3,2,4] => [1,2,4,3] => [1,2,4,3] => 3 = 2 + 1
[1,3,-2,4] => [1,3,2,4] => [1,2,4,3] => [1,2,4,3] => 3 = 2 + 1
[1,3,-2,-4] => [1,3,2,4] => [1,2,4,3] => [1,2,4,3] => 3 = 2 + 1
[1,-3,2,4] => [1,3,2,4] => [1,2,4,3] => [1,2,4,3] => 3 = 2 + 1
[1,-3,2,-4] => [1,3,2,4] => [1,2,4,3] => [1,2,4,3] => 3 = 2 + 1
[1,-3,-2,4] => [1,3,2,4] => [1,2,4,3] => [1,2,4,3] => 3 = 2 + 1
[1,-3,-2,-4] => [1,3,2,4] => [1,2,4,3] => [1,2,4,3] => 3 = 2 + 1
[-1,3,2,4] => [1,3,2,4] => [1,2,4,3] => [1,2,4,3] => 3 = 2 + 1
[-1,3,2,-4] => [1,3,2,4] => [1,2,4,3] => [1,2,4,3] => 3 = 2 + 1
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,2,3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,2,3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,2,3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,2,-3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,2,-3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,2,-3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,2,-3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,-2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,-2,3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,-2,3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,-2,3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,-2,-3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,-2,-3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,-2,-3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,-2,-3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,2,3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,2,3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,2,3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,2,-3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,2,-3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,2,-3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,2,-3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,-2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,-2,3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,-2,3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,-2,3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,-2,-3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,-2,-3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,-2,-3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[-1,-2,-3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 4 + 1
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,2,3,5,-4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,2,3,-5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,2,3,-5,-4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,2,-3,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,2,-3,5,-4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,2,-3,-5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,2,-3,-5,-4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,-2,3,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,-2,3,5,-4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,-2,3,-5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,-2,3,-5,-4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,-2,-3,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,-2,-3,5,-4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,-2,-3,-5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[1,-2,-3,-5,-4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[-1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
[-1,2,3,5,-4] => [1,2,3,5,4] => [2,3,4,1,5] => [2,3,4,1,5] => ? = 3 + 1
Description
The number of minimal elements in Bruhat order not less than the signed permutation.
The minimal elements in question are biGrassmannian, that is both the element and its inverse have at most one descent.
This is the size of the essential set of the signed permutation, see [1].
Matching statistic: St001624
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001624: Lattices ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 17%
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001624: Lattices ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 17%
Values
[1,2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[1,2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[1,-2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[1,-2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[-1,2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[-1,2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[-1,-2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[-1,-2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,3,4,2] => [1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ? = 2
[1,3,4,-2] => [1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ? = 2
[2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,-1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,-1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,-2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,-2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,-2,-1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,-2,-1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,-5,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,-5,2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
Description
The breadth of a lattice.
The '''breadth''' of a lattice is the least integer $b$ such that any join $x_1\vee x_2\vee\cdots\vee x_n$, with $n > b$, can be expressed as a join over a proper subset of $\{x_1,x_2,\ldots,x_n\}$.
Matching statistic: St001630
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 17%
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 17%
Values
[1,2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[1,2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[1,-2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[1,-2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[-1,2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[-1,2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[-1,-2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[-1,-2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,3,4,2] => [1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ? = 2
[1,3,4,-2] => [1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ? = 2
[2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,-1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,-1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,-2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,-2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,-2,-1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,-2,-1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,-5,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,-5,2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Matching statistic: St001878
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 17%
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 17%
Values
[1,2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[1,2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[1,-2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[1,-2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[-1,2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[-1,2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[-1,-2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[-1,-2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[-1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 3
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[-1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 2
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[-1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[1,3,4,2] => [1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ? = 2
[1,3,4,-2] => [1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ? = 2
[2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[2,-5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[-2,-5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,-1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,-1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,-2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,-2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,-2,-1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,-2,-1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,-5,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
[3,-5,2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
Matching statistic: St000327
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000327: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Mp00209: Permutations —pattern poset⟶ Posets
St000327: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Values
[1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,2,-3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,-2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,-2,-3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[-1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[-1,2,-3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[-1,-2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[-1,-2,-3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,-2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,-2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,-2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,-2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,-2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,-2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,-2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,-2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,2,4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,2,-4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,2,-4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,-2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,-2,4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,-2,-4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,-2,-4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,2,4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,2,-4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,2,-4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,-2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,-2,4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,-2,-4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,-2,-4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,-4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,-4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,-4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,-4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,-4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,-4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,-4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,-4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,4,2,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,4,2,-3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,-3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,-3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,-3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,-3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,-3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,-3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,-3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,-3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,-3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,-3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,-3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,-3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,-2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,-2,3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
Description
The number of cover relations in a poset.
Equivalently, this is also the number of edges in the Hasse diagram [1].
Matching statistic: St001637
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001637: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Mp00209: Permutations —pattern poset⟶ Posets
St001637: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Values
[1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,2,-3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,-2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,-2,-3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[-1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[-1,2,-3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[-1,-2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[-1,-2,-3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,-2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,-2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,-2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,-2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,-2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,-2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,-2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,-2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,2,4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,2,-4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,2,-4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,-2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,-2,4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,-2,-4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,-2,-4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,2,4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,2,-4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,2,-4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,-2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,-2,4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,-2,-4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,-2,-4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,-4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,-4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,-4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,-4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,-4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,-4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,-4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,-4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,4,2,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,4,2,-3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,-3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,-3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,-3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,-3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,-3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,-3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,-3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,-3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,-3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,-3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,-3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,-3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,-2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,-2,3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
Description
The number of (upper) dissectors of a poset.
Matching statistic: St001668
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001668: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Mp00209: Permutations —pattern poset⟶ Posets
St001668: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Values
[1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,2,-3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,-2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,-2,-3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[-1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[-1,2,-3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[-1,-2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[-1,-2,-3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 2
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,-2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,-2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,-2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,-2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,-2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,-2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,-2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-1,-2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,2,4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,2,-4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,2,-4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,-2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,-2,4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,-2,-4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,-2,-4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,2,4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,2,-4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,2,-4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,-2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,-2,4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,-2,-4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[-1,-2,-4,-3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,-4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,3,-4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,-4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,-3,-4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,-4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,3,-4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,-4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[-1,-3,-4,-2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,4,2,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,4,2,-3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 2
[1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,-3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,-3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,-3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,2,-3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,-3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,-3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,-3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,-2,-3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,-3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,-3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,-3,-4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,2,-3,-4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,-2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-1,-2,3,4,-5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
Description
The number of points of the poset minus the width of the poset.
The following 4 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001754The number of tolerances of a finite lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001879The 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.
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