searching the database
Your data matches 20 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000673
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
St000673: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000673: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => 0
[2,1] => [2,1] => 2
[1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => 2
[2,1,3] => [2,1,3] => 2
[2,3,1] => [3,2,1] => 2
[3,1,2] => [3,2,1] => 2
[3,2,1] => [3,2,1] => 2
[1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => 2
[1,3,2,4] => [1,3,2,4] => 2
[1,3,4,2] => [1,4,3,2] => 2
[1,4,2,3] => [1,4,3,2] => 2
[1,4,3,2] => [1,4,3,2] => 2
[2,1,3,4] => [2,1,3,4] => 2
[2,1,4,3] => [2,1,4,3] => 4
[2,3,1,4] => [3,2,1,4] => 2
[2,3,4,1] => [4,2,3,1] => 2
[2,4,1,3] => [3,4,1,2] => 4
[2,4,3,1] => [4,3,2,1] => 4
[3,1,2,4] => [3,2,1,4] => 2
[3,1,4,2] => [4,2,3,1] => 2
[3,2,1,4] => [3,2,1,4] => 2
[3,2,4,1] => [4,2,3,1] => 2
[3,4,1,2] => [4,3,2,1] => 4
[3,4,2,1] => [4,3,2,1] => 4
[4,1,2,3] => [4,2,3,1] => 2
[4,1,3,2] => [4,2,3,1] => 2
[4,2,1,3] => [4,3,2,1] => 4
[4,2,3,1] => [4,3,2,1] => 4
[4,3,1,2] => [4,3,2,1] => 4
[4,3,2,1] => [4,3,2,1] => 4
[1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => 2
[1,2,4,3,5] => [1,2,4,3,5] => 2
[1,2,4,5,3] => [1,2,5,4,3] => 2
[1,2,5,3,4] => [1,2,5,4,3] => 2
[1,2,5,4,3] => [1,2,5,4,3] => 2
[1,3,2,4,5] => [1,3,2,4,5] => 2
[1,3,2,5,4] => [1,3,2,5,4] => 4
[1,3,4,2,5] => [1,4,3,2,5] => 2
[1,3,4,5,2] => [1,5,3,4,2] => 2
[1,3,5,2,4] => [1,4,5,2,3] => 4
[1,3,5,4,2] => [1,5,4,3,2] => 4
[1,4,2,3,5] => [1,4,3,2,5] => 2
[1,4,2,5,3] => [1,5,3,4,2] => 2
[1,4,3,2,5] => [1,4,3,2,5] => 2
[1,4,3,5,2] => [1,5,3,4,2] => 2
[1,4,5,2,3] => [1,5,4,3,2] => 4
[1,4,5,3,2] => [1,5,4,3,2] => 4
Description
The number of non-fixed points of a permutation.
In other words, this statistic is $n$ minus the number of fixed points ([[St000022]]) of $\pi$.
Matching statistic: St000235
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
St000235: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
St000235: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [2,1] => 0
[2,1] => [2,1] => [1,2] => 2
[1,2,3] => [1,2,3] => [2,3,1] => 0
[1,3,2] => [1,3,2] => [3,2,1] => 2
[2,1,3] => [2,1,3] => [1,3,2] => 2
[2,3,1] => [3,2,1] => [2,1,3] => 2
[3,1,2] => [3,2,1] => [2,1,3] => 2
[3,2,1] => [3,2,1] => [2,1,3] => 2
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => 0
[1,2,4,3] => [1,2,4,3] => [2,4,3,1] => 2
[1,3,2,4] => [1,3,2,4] => [3,2,4,1] => 2
[1,3,4,2] => [1,4,3,2] => [4,3,2,1] => 2
[1,4,2,3] => [1,4,3,2] => [4,3,2,1] => 2
[1,4,3,2] => [1,4,3,2] => [4,3,2,1] => 2
[2,1,3,4] => [2,1,3,4] => [1,3,4,2] => 2
[2,1,4,3] => [2,1,4,3] => [1,4,3,2] => 4
[2,3,1,4] => [3,2,1,4] => [2,1,4,3] => 2
[2,3,4,1] => [4,2,3,1] => [2,3,1,4] => 2
[2,4,1,3] => [3,4,1,2] => [4,1,2,3] => 4
[2,4,3,1] => [4,3,2,1] => [3,2,1,4] => 4
[3,1,2,4] => [3,2,1,4] => [2,1,4,3] => 2
[3,1,4,2] => [4,2,3,1] => [2,3,1,4] => 2
[3,2,1,4] => [3,2,1,4] => [2,1,4,3] => 2
[3,2,4,1] => [4,2,3,1] => [2,3,1,4] => 2
[3,4,1,2] => [4,3,2,1] => [3,2,1,4] => 4
[3,4,2,1] => [4,3,2,1] => [3,2,1,4] => 4
[4,1,2,3] => [4,2,3,1] => [2,3,1,4] => 2
[4,1,3,2] => [4,2,3,1] => [2,3,1,4] => 2
[4,2,1,3] => [4,3,2,1] => [3,2,1,4] => 4
[4,2,3,1] => [4,3,2,1] => [3,2,1,4] => 4
[4,3,1,2] => [4,3,2,1] => [3,2,1,4] => 4
[4,3,2,1] => [4,3,2,1] => [3,2,1,4] => 4
[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,5,4,1] => 2
[1,2,4,3,5] => [1,2,4,3,5] => [2,4,3,5,1] => 2
[1,2,4,5,3] => [1,2,5,4,3] => [2,5,4,3,1] => 2
[1,2,5,3,4] => [1,2,5,4,3] => [2,5,4,3,1] => 2
[1,2,5,4,3] => [1,2,5,4,3] => [2,5,4,3,1] => 2
[1,3,2,4,5] => [1,3,2,4,5] => [3,2,4,5,1] => 2
[1,3,2,5,4] => [1,3,2,5,4] => [3,2,5,4,1] => 4
[1,3,4,2,5] => [1,4,3,2,5] => [4,3,2,5,1] => 2
[1,3,4,5,2] => [1,5,3,4,2] => [5,3,4,2,1] => 2
[1,3,5,2,4] => [1,4,5,2,3] => [4,5,2,3,1] => 4
[1,3,5,4,2] => [1,5,4,3,2] => [5,4,3,2,1] => 4
[1,4,2,3,5] => [1,4,3,2,5] => [4,3,2,5,1] => 2
[1,4,2,5,3] => [1,5,3,4,2] => [5,3,4,2,1] => 2
[1,4,3,2,5] => [1,4,3,2,5] => [4,3,2,5,1] => 2
[1,4,3,5,2] => [1,5,3,4,2] => [5,3,4,2,1] => 2
[1,4,5,2,3] => [1,5,4,3,2] => [5,4,3,2,1] => 4
[1,4,5,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => 4
Description
The number of indices that are not cyclical small weak excedances.
A cyclical small weak excedance is an index $i < n$ such that $\pi_i = i+1$, or the index $i = n$ if $\pi_n = 1$.
Matching statistic: St001248
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
St001248: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00108: Permutations —cycle type⟶ Integer partitions
St001248: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,1]
=> 0
[2,1] => [2,1] => [2]
=> 2
[1,2,3] => [1,2,3] => [1,1,1]
=> 0
[1,3,2] => [1,3,2] => [2,1]
=> 2
[2,1,3] => [2,1,3] => [2,1]
=> 2
[2,3,1] => [3,2,1] => [2,1]
=> 2
[3,1,2] => [3,2,1] => [2,1]
=> 2
[3,2,1] => [3,2,1] => [2,1]
=> 2
[1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> 0
[1,2,4,3] => [1,2,4,3] => [2,1,1]
=> 2
[1,3,2,4] => [1,3,2,4] => [2,1,1]
=> 2
[1,3,4,2] => [1,4,3,2] => [2,1,1]
=> 2
[1,4,2,3] => [1,4,3,2] => [2,1,1]
=> 2
[1,4,3,2] => [1,4,3,2] => [2,1,1]
=> 2
[2,1,3,4] => [2,1,3,4] => [2,1,1]
=> 2
[2,1,4,3] => [2,1,4,3] => [2,2]
=> 4
[2,3,1,4] => [3,2,1,4] => [2,1,1]
=> 2
[2,3,4,1] => [4,2,3,1] => [2,1,1]
=> 2
[2,4,1,3] => [3,4,1,2] => [2,2]
=> 4
[2,4,3,1] => [4,3,2,1] => [2,2]
=> 4
[3,1,2,4] => [3,2,1,4] => [2,1,1]
=> 2
[3,1,4,2] => [4,2,3,1] => [2,1,1]
=> 2
[3,2,1,4] => [3,2,1,4] => [2,1,1]
=> 2
[3,2,4,1] => [4,2,3,1] => [2,1,1]
=> 2
[3,4,1,2] => [4,3,2,1] => [2,2]
=> 4
[3,4,2,1] => [4,3,2,1] => [2,2]
=> 4
[4,1,2,3] => [4,2,3,1] => [2,1,1]
=> 2
[4,1,3,2] => [4,2,3,1] => [2,1,1]
=> 2
[4,2,1,3] => [4,3,2,1] => [2,2]
=> 4
[4,2,3,1] => [4,3,2,1] => [2,2]
=> 4
[4,3,1,2] => [4,3,2,1] => [2,2]
=> 4
[4,3,2,1] => [4,3,2,1] => [2,2]
=> 4
[1,2,3,4,5] => [1,2,3,4,5] => [1,1,1,1,1]
=> 0
[1,2,3,5,4] => [1,2,3,5,4] => [2,1,1,1]
=> 2
[1,2,4,3,5] => [1,2,4,3,5] => [2,1,1,1]
=> 2
[1,2,4,5,3] => [1,2,5,4,3] => [2,1,1,1]
=> 2
[1,2,5,3,4] => [1,2,5,4,3] => [2,1,1,1]
=> 2
[1,2,5,4,3] => [1,2,5,4,3] => [2,1,1,1]
=> 2
[1,3,2,4,5] => [1,3,2,4,5] => [2,1,1,1]
=> 2
[1,3,2,5,4] => [1,3,2,5,4] => [2,2,1]
=> 4
[1,3,4,2,5] => [1,4,3,2,5] => [2,1,1,1]
=> 2
[1,3,4,5,2] => [1,5,3,4,2] => [2,1,1,1]
=> 2
[1,3,5,2,4] => [1,4,5,2,3] => [2,2,1]
=> 4
[1,3,5,4,2] => [1,5,4,3,2] => [2,2,1]
=> 4
[1,4,2,3,5] => [1,4,3,2,5] => [2,1,1,1]
=> 2
[1,4,2,5,3] => [1,5,3,4,2] => [2,1,1,1]
=> 2
[1,4,3,2,5] => [1,4,3,2,5] => [2,1,1,1]
=> 2
[1,4,3,5,2] => [1,5,3,4,2] => [2,1,1,1]
=> 2
[1,4,5,2,3] => [1,5,4,3,2] => [2,2,1]
=> 4
[1,4,5,3,2] => [1,5,4,3,2] => [2,2,1]
=> 4
Description
Sum of the even parts of a partition.
Matching statistic: St001279
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
St001279: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00108: Permutations —cycle type⟶ Integer partitions
St001279: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,1]
=> 0
[2,1] => [2,1] => [2]
=> 2
[1,2,3] => [1,2,3] => [1,1,1]
=> 0
[1,3,2] => [1,3,2] => [2,1]
=> 2
[2,1,3] => [2,1,3] => [2,1]
=> 2
[2,3,1] => [3,2,1] => [2,1]
=> 2
[3,1,2] => [3,2,1] => [2,1]
=> 2
[3,2,1] => [3,2,1] => [2,1]
=> 2
[1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> 0
[1,2,4,3] => [1,2,4,3] => [2,1,1]
=> 2
[1,3,2,4] => [1,3,2,4] => [2,1,1]
=> 2
[1,3,4,2] => [1,4,3,2] => [2,1,1]
=> 2
[1,4,2,3] => [1,4,3,2] => [2,1,1]
=> 2
[1,4,3,2] => [1,4,3,2] => [2,1,1]
=> 2
[2,1,3,4] => [2,1,3,4] => [2,1,1]
=> 2
[2,1,4,3] => [2,1,4,3] => [2,2]
=> 4
[2,3,1,4] => [3,2,1,4] => [2,1,1]
=> 2
[2,3,4,1] => [4,2,3,1] => [2,1,1]
=> 2
[2,4,1,3] => [3,4,1,2] => [2,2]
=> 4
[2,4,3,1] => [4,3,2,1] => [2,2]
=> 4
[3,1,2,4] => [3,2,1,4] => [2,1,1]
=> 2
[3,1,4,2] => [4,2,3,1] => [2,1,1]
=> 2
[3,2,1,4] => [3,2,1,4] => [2,1,1]
=> 2
[3,2,4,1] => [4,2,3,1] => [2,1,1]
=> 2
[3,4,1,2] => [4,3,2,1] => [2,2]
=> 4
[3,4,2,1] => [4,3,2,1] => [2,2]
=> 4
[4,1,2,3] => [4,2,3,1] => [2,1,1]
=> 2
[4,1,3,2] => [4,2,3,1] => [2,1,1]
=> 2
[4,2,1,3] => [4,3,2,1] => [2,2]
=> 4
[4,2,3,1] => [4,3,2,1] => [2,2]
=> 4
[4,3,1,2] => [4,3,2,1] => [2,2]
=> 4
[4,3,2,1] => [4,3,2,1] => [2,2]
=> 4
[1,2,3,4,5] => [1,2,3,4,5] => [1,1,1,1,1]
=> 0
[1,2,3,5,4] => [1,2,3,5,4] => [2,1,1,1]
=> 2
[1,2,4,3,5] => [1,2,4,3,5] => [2,1,1,1]
=> 2
[1,2,4,5,3] => [1,2,5,4,3] => [2,1,1,1]
=> 2
[1,2,5,3,4] => [1,2,5,4,3] => [2,1,1,1]
=> 2
[1,2,5,4,3] => [1,2,5,4,3] => [2,1,1,1]
=> 2
[1,3,2,4,5] => [1,3,2,4,5] => [2,1,1,1]
=> 2
[1,3,2,5,4] => [1,3,2,5,4] => [2,2,1]
=> 4
[1,3,4,2,5] => [1,4,3,2,5] => [2,1,1,1]
=> 2
[1,3,4,5,2] => [1,5,3,4,2] => [2,1,1,1]
=> 2
[1,3,5,2,4] => [1,4,5,2,3] => [2,2,1]
=> 4
[1,3,5,4,2] => [1,5,4,3,2] => [2,2,1]
=> 4
[1,4,2,3,5] => [1,4,3,2,5] => [2,1,1,1]
=> 2
[1,4,2,5,3] => [1,5,3,4,2] => [2,1,1,1]
=> 2
[1,4,3,2,5] => [1,4,3,2,5] => [2,1,1,1]
=> 2
[1,4,3,5,2] => [1,5,3,4,2] => [2,1,1,1]
=> 2
[1,4,5,2,3] => [1,5,4,3,2] => [2,2,1]
=> 4
[1,4,5,3,2] => [1,5,4,3,2] => [2,2,1]
=> 4
Description
The sum of the parts of an integer partition that are at least two.
Matching statistic: St000824
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St000824: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St000824: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => [2,1] => 2
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,3,2] => [1,3,2] => 2
[2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 2
[2,3,1] => [3,2,1] => [2,3,1] => [1,3,2] => 2
[3,1,2] => [3,2,1] => [2,3,1] => [1,3,2] => 2
[3,2,1] => [3,2,1] => [2,3,1] => [1,3,2] => 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [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] => [1,3,2,4] => 2
[1,3,4,2] => [1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 2
[1,4,2,3] => [1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 2
[1,4,3,2] => [1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 2
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 2
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 4
[2,3,1,4] => [3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 2
[2,3,4,1] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[2,4,1,3] => [3,4,1,2] => [3,1,4,2] => [2,1,4,3] => 4
[2,4,3,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[3,1,2,4] => [3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 2
[3,1,4,2] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[3,2,1,4] => [3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 2
[3,2,4,1] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[3,4,1,2] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[3,4,2,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,1,2,3] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[4,1,3,2] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[4,2,1,3] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,2,3,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,3,1,2] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,3,2,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 2
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 2
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => 2
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => 2
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 4
[1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => 2
[1,3,4,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => 2
[1,3,5,2,4] => [1,4,5,2,3] => [1,4,2,5,3] => [1,3,2,5,4] => 4
[1,3,5,4,2] => [1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => 4
[1,4,2,3,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => 2
[1,4,2,5,3] => [1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => 2
[1,4,3,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => 2
[1,4,3,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => 2
[1,4,5,2,3] => [1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => 4
[1,4,5,3,2] => [1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => 4
Description
The sum of the number of descents and the number of recoils of a permutation.
This statistic is the sum of [[St000021]] and [[St000354]].
Matching statistic: St000828
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St000828: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St000828: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => [2,1] => 2
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,3,2] => [1,3,2] => 2
[2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 2
[2,3,1] => [3,2,1] => [2,3,1] => [1,3,2] => 2
[3,1,2] => [3,2,1] => [2,3,1] => [1,3,2] => 2
[3,2,1] => [3,2,1] => [2,3,1] => [1,3,2] => 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [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] => [1,3,2,4] => 2
[1,3,4,2] => [1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 2
[1,4,2,3] => [1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 2
[1,4,3,2] => [1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 2
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 2
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 4
[2,3,1,4] => [3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 2
[2,3,4,1] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[2,4,1,3] => [3,4,1,2] => [3,1,4,2] => [2,1,4,3] => 4
[2,4,3,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[3,1,2,4] => [3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 2
[3,1,4,2] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[3,2,1,4] => [3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 2
[3,2,4,1] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[3,4,1,2] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[3,4,2,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,1,2,3] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[4,1,3,2] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[4,2,1,3] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,2,3,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,3,1,2] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,3,2,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 2
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 2
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => 2
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => 2
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 4
[1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => 2
[1,3,4,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => 2
[1,3,5,2,4] => [1,4,5,2,3] => [1,4,2,5,3] => [1,3,2,5,4] => 4
[1,3,5,4,2] => [1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => 4
[1,4,2,3,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => 2
[1,4,2,5,3] => [1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => 2
[1,4,3,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => 2
[1,4,3,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => 2
[1,4,5,2,3] => [1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => 4
[1,4,5,3,2] => [1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => 4
Description
The spearman's rho of a permutation and the identity permutation.
This is, for a permutation $\pi$ of $n$, given by $\sum_{i=1}^n (\pi(i)−i)^2$.
Matching statistic: St000830
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St000830: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St000830: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => [2,1] => 2
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,3,2] => [1,3,2] => 2
[2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 2
[2,3,1] => [3,2,1] => [2,3,1] => [1,3,2] => 2
[3,1,2] => [3,2,1] => [2,3,1] => [1,3,2] => 2
[3,2,1] => [3,2,1] => [2,3,1] => [1,3,2] => 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [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] => [1,3,2,4] => 2
[1,3,4,2] => [1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 2
[1,4,2,3] => [1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 2
[1,4,3,2] => [1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 2
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 2
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 4
[2,3,1,4] => [3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 2
[2,3,4,1] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[2,4,1,3] => [3,4,1,2] => [3,1,4,2] => [2,1,4,3] => 4
[2,4,3,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[3,1,2,4] => [3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 2
[3,1,4,2] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[3,2,1,4] => [3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 2
[3,2,4,1] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[3,4,1,2] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[3,4,2,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,1,2,3] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[4,1,3,2] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[4,2,1,3] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,2,3,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,3,1,2] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,3,2,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 2
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 2
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => 2
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => 2
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 4
[1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => 2
[1,3,4,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => 2
[1,3,5,2,4] => [1,4,5,2,3] => [1,4,2,5,3] => [1,3,2,5,4] => 4
[1,3,5,4,2] => [1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => 4
[1,4,2,3,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => 2
[1,4,2,5,3] => [1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => 2
[1,4,3,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => 2
[1,4,3,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => 2
[1,4,5,2,3] => [1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => 4
[1,4,5,3,2] => [1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => 4
Description
The total displacement of a permutation.
This is, for a permutation $\pi$ of $n$, given by $\sum_{i = 1}^n | \pi(i) - i |.$
This is twice the statistic [[St000029]] and can be found in [3, Problem 5.1.1.28] and also in [1, 2].
Matching statistic: St001005
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St001005: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St001005: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => [2,1] => 2
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,3,2] => [1,3,2] => 2
[2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 2
[2,3,1] => [3,2,1] => [2,3,1] => [1,3,2] => 2
[3,1,2] => [3,2,1] => [2,3,1] => [1,3,2] => 2
[3,2,1] => [3,2,1] => [2,3,1] => [1,3,2] => 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [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] => [1,3,2,4] => 2
[1,3,4,2] => [1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 2
[1,4,2,3] => [1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 2
[1,4,3,2] => [1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 2
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 2
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 4
[2,3,1,4] => [3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 2
[2,3,4,1] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[2,4,1,3] => [3,4,1,2] => [3,1,4,2] => [2,1,4,3] => 4
[2,4,3,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[3,1,2,4] => [3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 2
[3,1,4,2] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[3,2,1,4] => [3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 2
[3,2,4,1] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[3,4,1,2] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[3,4,2,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,1,2,3] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[4,1,3,2] => [4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 2
[4,2,1,3] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,2,3,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,3,1,2] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[4,3,2,1] => [4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 4
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 2
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 2
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => 2
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => 2
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 4
[1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => 2
[1,3,4,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => 2
[1,3,5,2,4] => [1,4,5,2,3] => [1,4,2,5,3] => [1,3,2,5,4] => 4
[1,3,5,4,2] => [1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => 4
[1,4,2,3,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => 2
[1,4,2,5,3] => [1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => 2
[1,4,3,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => 2
[1,4,3,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => 2
[1,4,5,2,3] => [1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => 4
[1,4,5,3,2] => [1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => 4
Description
The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both.
Matching statistic: St001458
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001458: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001458: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,2] => ([],2)
=> 0
[2,1] => [2,1] => [2,1] => ([(0,1)],2)
=> 2
[1,2,3] => [1,2,3] => [1,2,3] => ([],3)
=> 0
[1,3,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
=> 2
[2,1,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
=> 2
[2,3,1] => [3,2,1] => [2,3,1] => ([(0,2),(1,2)],3)
=> 2
[3,1,2] => [3,2,1] => [2,3,1] => ([(0,2),(1,2)],3)
=> 2
[3,2,1] => [3,2,1] => [2,3,1] => ([(0,2),(1,2)],3)
=> 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([],4)
=> 0
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
=> 2
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> 2
[1,3,4,2] => [1,4,3,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> 2
[1,4,2,3] => [1,4,3,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> 2
[1,4,3,2] => [1,4,3,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> 2
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
=> 2
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> 4
[2,3,1,4] => [3,2,1,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> 2
[2,3,4,1] => [4,2,3,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[2,4,1,3] => [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 4
[2,4,3,1] => [4,3,2,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,1,2,4] => [3,2,1,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> 2
[3,1,4,2] => [4,2,3,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[3,2,1,4] => [3,2,1,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> 2
[3,2,4,1] => [4,2,3,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[3,4,1,2] => [4,3,2,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[3,4,2,1] => [4,3,2,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,1,2,3] => [4,2,3,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[4,1,3,2] => [4,2,3,1] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[4,2,1,3] => [4,3,2,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,2,3,1] => [4,3,2,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,3,1,2] => [4,3,2,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[4,3,2,1] => [4,3,2,1] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 4
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([],5)
=> 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(3,4)],5)
=> 2
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => ([(3,4)],5)
=> 2
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> 2
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> 2
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => ([(3,4)],5)
=> 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
=> 4
[1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> 2
[1,3,4,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> 2
[1,3,5,2,4] => [1,4,5,2,3] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> 4
[1,3,5,4,2] => [1,5,4,3,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 4
[1,4,2,3,5] => [1,4,3,2,5] => [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> 2
[1,4,2,5,3] => [1,5,3,4,2] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> 2
[1,4,3,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> 2
[1,4,3,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> 2
[1,4,5,2,3] => [1,5,4,3,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 4
[1,4,5,3,2] => [1,5,4,3,2] => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 4
Description
The rank of the adjacency matrix of a graph.
Matching statistic: St000264
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 36%●distinct values known / distinct values provided: 25%
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 36%●distinct values known / distinct values provided: 25%
Values
[1,2] => [1,2] => [2,1] => ([(0,1)],2)
=> ? ∊ {0,2}
[2,1] => [2,1] => [1,2] => ([],2)
=> ? ∊ {0,2}
[1,2,3] => [1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> ? ∊ {0,2,2,2,2,2}
[1,3,2] => [1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> ? ∊ {0,2,2,2,2,2}
[2,1,3] => [2,1,3] => [3,1,2] => ([(0,2),(1,2)],3)
=> ? ∊ {0,2,2,2,2,2}
[2,3,1] => [2,3,1] => [1,3,2] => ([(1,2)],3)
=> ? ∊ {0,2,2,2,2,2}
[3,1,2] => [3,1,2] => [2,1,3] => ([(1,2)],3)
=> ? ∊ {0,2,2,2,2,2}
[3,2,1] => [3,2,1] => [1,2,3] => ([],3)
=> ? ∊ {0,2,2,2,2,2}
[1,2,3,4] => [1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[1,2,4,3] => [1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[1,3,2,4] => [1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[1,3,4,2] => [1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[1,4,2,3] => [1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[1,4,3,2] => [1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[2,1,3,4] => [2,1,4,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
[2,1,4,3] => [2,1,4,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
[2,3,1,4] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[2,3,4,1] => [2,4,3,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[2,4,1,3] => [2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[2,4,3,1] => [2,4,3,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[3,1,2,4] => [3,1,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[3,1,4,2] => [3,1,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[3,2,1,4] => [3,2,1,4] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[3,2,4,1] => [3,2,4,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[3,4,1,2] => [3,4,1,2] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[3,4,2,1] => [3,4,2,1] => [1,2,4,3] => ([(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[4,1,2,3] => [4,1,3,2] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[4,1,3,2] => [4,1,3,2] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[4,2,1,3] => [4,2,1,3] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[4,2,3,1] => [4,2,3,1] => [1,3,2,4] => ([(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[4,3,1,2] => [4,3,1,2] => [2,1,3,4] => ([(2,3)],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[4,3,2,1] => [4,3,2,1] => [1,2,3,4] => ([],4)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4}
[1,2,3,4,5] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,2,3,5,4] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,2,4,3,5] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,2,4,5,3] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,2,5,3,4] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,2,5,4,3] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,3,2,4,5] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,3,2,5,4] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,3,4,2,5] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,3,4,5,2] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,3,5,2,4] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,3,5,4,2] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,4,2,3,5] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,4,2,5,3] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,4,3,2,5] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,4,3,5,2] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,4,5,2,3] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,4,5,3,2] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,5,2,3,4] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[1,5,2,4,3] => [1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? ∊ {0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}
[2,1,3,4,5] => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[2,1,3,5,4] => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[2,1,4,3,5] => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[2,1,4,5,3] => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[2,1,5,3,4] => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[2,1,5,4,3] => [2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[2,3,1,4,5] => [2,5,1,4,3] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[2,3,1,5,4] => [2,5,1,4,3] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[2,4,1,3,5] => [2,5,1,4,3] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[2,4,1,5,3] => [2,5,1,4,3] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[2,5,1,3,4] => [2,5,1,4,3] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[2,5,1,4,3] => [2,5,1,4,3] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[3,1,2,4,5] => [3,1,5,4,2] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[3,1,2,5,4] => [3,1,5,4,2] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[3,1,4,2,5] => [3,1,5,4,2] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[3,1,4,5,2] => [3,1,5,4,2] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[3,1,5,2,4] => [3,1,5,4,2] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[3,1,5,4,2] => [3,1,5,4,2] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[3,2,1,4,5] => [3,2,1,5,4] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[3,2,1,5,4] => [3,2,1,5,4] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[3,2,4,1,5] => [3,2,5,1,4] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[3,2,4,5,1] => [3,2,5,4,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[3,2,5,1,4] => [3,2,5,1,4] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[3,2,5,4,1] => [3,2,5,4,1] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[4,2,1,3,5] => [4,2,1,5,3] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[4,2,1,5,3] => [4,2,1,5,3] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[5,2,1,3,4] => [5,2,1,4,3] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[5,2,1,4,3] => [5,2,1,4,3] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[2,1,3,4,5,6] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,3,4,6,5] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,3,5,4,6] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,3,5,6,4] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,3,6,4,5] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,3,6,5,4] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,4,3,5,6] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,4,3,6,5] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,4,5,3,6] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,4,5,6,3] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,4,6,3,5] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,4,6,5,3] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,5,3,4,6] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,5,3,6,4] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,5,4,3,6] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,5,4,6,3] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,5,6,4,3] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,6,3,4,5] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
[2,1,6,3,5,4] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
The following 10 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000896The number of zeros on the main diagonal of an alternating sign matrix. St000422The energy of a graph, if it is integral. St000708The product of the parts of an integer partition. St001527The cyclic permutation representation number of an integer partition. St001892The flag excedance statistic of a signed permutation. St001893The flag descent of a signed permutation. St000454The largest eigenvalue of a graph if it is integral. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!