searching the database
Your data matches 4 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: St000374
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St000374: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00252: Permutations —restriction⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St000374: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> [1] => [] => [] => 0
[1,0,1,0]
=> [1,2] => [1] => [1] => 0
[1,1,0,0]
=> [2,1] => [1] => [1] => 0
[1,0,1,0,1,0]
=> [1,2,3] => [1,2] => [1,2] => 0
[1,0,1,1,0,0]
=> [1,3,2] => [1,2] => [1,2] => 0
[1,1,0,0,1,0]
=> [2,1,3] => [2,1] => [2,1] => 1
[1,1,0,1,0,0]
=> [2,3,1] => [2,1] => [2,1] => 1
[1,1,1,0,0,0]
=> [3,1,2] => [1,2] => [1,2] => 0
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [1,3,2] => [3,1,2] => 2
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [1,3,2] => [3,1,2] => 2
[1,0,1,1,1,0,0,0]
=> [1,4,2,3] => [1,2,3] => [1,2,3] => 0
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,3] => [2,3,1] => 1
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,1,3] => [2,3,1] => 1
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => [2,3,1] => [2,1,3] => 1
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => [2,3,1] => [2,1,3] => 1
[1,1,0,1,1,0,0,0]
=> [2,4,1,3] => [2,1,3] => [2,3,1] => 1
[1,1,1,0,0,0,1,0]
=> [3,1,2,4] => [3,1,2] => [1,3,2] => 1
[1,1,1,0,0,1,0,0]
=> [3,1,4,2] => [3,1,2] => [1,3,2] => 1
[1,1,1,0,1,0,0,0]
=> [3,4,1,2] => [3,1,2] => [1,3,2] => 1
[1,1,1,1,0,0,0,0]
=> [4,1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [1,2,4,3] => [4,1,2,3] => 3
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [1,2,4,3] => [4,1,2,3] => 3
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [1,3,4,2] => [3,1,2,4] => 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [1,3,4,2] => [3,1,2,4] => 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,2,3,5] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,2,5,3] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,4,5,2,3] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,1,4,3] => [2,1,4,3] => 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [2,1,4,3] => [2,1,4,3] => 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,3,4] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [2,3,4,1] => [2,1,3,4] => 1
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [2,3,4,1] => [2,1,3,4] => 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,5,3] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,1,3,4] => [2,1,3,4] => [2,3,4,1] => 1
Description
The number of exclusive right-to-left minima of a permutation.
This is the number of right-to-left minima that are not left-to-right maxima.
This is also the number of non weak exceedences of a permutation that are also not mid-points of a decreasing subsequence of length 3.
Given a permutation $\pi = [\pi_1,\ldots,\pi_n]$, this statistic counts the number of position $j$ such that $\pi_j < j$ and there do not exist indices $i,k$ with $i < j < k$ and $\pi_i > \pi_j > \pi_k$.
See also [[St000213]] and [[St000119]].
Matching statistic: St000703
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St000703: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00252: Permutations —restriction⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St000703: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> [1] => [] => [] => 0
[1,0,1,0]
=> [1,2] => [1] => [1] => 0
[1,1,0,0]
=> [2,1] => [1] => [1] => 0
[1,0,1,0,1,0]
=> [1,2,3] => [1,2] => [1,2] => 0
[1,0,1,1,0,0]
=> [1,3,2] => [1,2] => [1,2] => 0
[1,1,0,0,1,0]
=> [2,1,3] => [2,1] => [2,1] => 1
[1,1,0,1,0,0]
=> [2,3,1] => [2,1] => [2,1] => 1
[1,1,1,0,0,0]
=> [3,1,2] => [1,2] => [1,2] => 0
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [1,3,2] => [3,1,2] => 2
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [1,3,2] => [3,1,2] => 2
[1,0,1,1,1,0,0,0]
=> [1,4,2,3] => [1,2,3] => [1,2,3] => 0
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,3] => [2,3,1] => 1
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,1,3] => [2,3,1] => 1
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => [2,3,1] => [2,1,3] => 1
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => [2,3,1] => [2,1,3] => 1
[1,1,0,1,1,0,0,0]
=> [2,4,1,3] => [2,1,3] => [2,3,1] => 1
[1,1,1,0,0,0,1,0]
=> [3,1,2,4] => [3,1,2] => [1,3,2] => 1
[1,1,1,0,0,1,0,0]
=> [3,1,4,2] => [3,1,2] => [1,3,2] => 1
[1,1,1,0,1,0,0,0]
=> [3,4,1,2] => [3,1,2] => [1,3,2] => 1
[1,1,1,1,0,0,0,0]
=> [4,1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [1,2,4,3] => [4,1,2,3] => 3
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [1,2,4,3] => [4,1,2,3] => 3
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [1,3,4,2] => [3,1,2,4] => 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [1,3,4,2] => [3,1,2,4] => 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,2,3,5] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,2,5,3] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,4,5,2,3] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,1,4,3] => [2,1,4,3] => 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [2,1,4,3] => [2,1,4,3] => 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,3,4] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [2,3,4,1] => [2,1,3,4] => 1
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [2,3,4,1] => [2,1,3,4] => 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,5,3] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,1,3,4] => [2,1,3,4] => [2,3,4,1] => 1
Description
The number of deficiencies of a permutation.
This is defined as
$$\operatorname{dec}(\sigma)=\#\{i:\sigma(i) < i\}.$$
The number of exceedances is [[St000155]].
Matching statistic: St000337
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St000337: Permutations ⟶ ℤResult quality: 84% ●values known / values provided: 84%●distinct values known / distinct values provided: 100%
Mp00252: Permutations —restriction⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St000337: Permutations ⟶ ℤResult quality: 84% ●values known / values provided: 84%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> [1] => [] => [] => 0
[1,0,1,0]
=> [1,2] => [1] => [1] => 0
[1,1,0,0]
=> [2,1] => [1] => [1] => 0
[1,0,1,0,1,0]
=> [1,2,3] => [1,2] => [1,2] => 0
[1,0,1,1,0,0]
=> [1,3,2] => [1,2] => [1,2] => 0
[1,1,0,0,1,0]
=> [2,1,3] => [2,1] => [2,1] => 1
[1,1,0,1,0,0]
=> [2,3,1] => [2,1] => [2,1] => 1
[1,1,1,0,0,0]
=> [3,1,2] => [1,2] => [1,2] => 0
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [1,3,2] => [3,1,2] => 2
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [1,3,2] => [3,1,2] => 2
[1,0,1,1,1,0,0,0]
=> [1,4,2,3] => [1,2,3] => [1,2,3] => 0
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,3] => [2,3,1] => 1
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,1,3] => [2,3,1] => 1
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => [2,3,1] => [2,1,3] => 1
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => [2,3,1] => [2,1,3] => 1
[1,1,0,1,1,0,0,0]
=> [2,4,1,3] => [2,1,3] => [2,3,1] => 1
[1,1,1,0,0,0,1,0]
=> [3,1,2,4] => [3,1,2] => [1,3,2] => 1
[1,1,1,0,0,1,0,0]
=> [3,1,4,2] => [3,1,2] => [1,3,2] => 1
[1,1,1,0,1,0,0,0]
=> [3,4,1,2] => [3,1,2] => [1,3,2] => 1
[1,1,1,1,0,0,0,0]
=> [4,1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [1,2,4,3] => [4,1,2,3] => 3
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [1,2,4,3] => [4,1,2,3] => 3
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [1,3,4,2] => [3,1,2,4] => 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [1,3,4,2] => [3,1,2,4] => 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,2,3,5] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,2,5,3] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,4,5,2,3] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,1,4,3] => [2,1,4,3] => 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [2,1,4,3] => [2,1,4,3] => 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,3,4] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [2,3,4,1] => [2,1,3,4] => 1
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [2,3,4,1] => [2,1,3,4] => 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,5,3] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,1,3,4] => [2,1,3,4] => [2,3,4,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7] => [1,2,5,3,4,6,7] => ? = 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,2,3,5,4,8,6,7] => [1,2,3,5,4,6,7] => [1,2,5,3,4,6,7] => ? = 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7] => [1,2,6,3,4,5,7] => ? = 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,2,3,6,4,8,5,7] => [1,2,3,6,4,5,7] => [1,2,6,3,4,5,7] => ? = 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ? = 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,2,3,7,4,5,8,6] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ? = 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,2,3,7,4,8,5,6] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ? = 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => ? = 3
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,2,4,3,8,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,5,3,6,7] => ? = 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,2,5,3,8,4,6,7] => [1,2,5,3,4,6,7] => [1,2,3,5,4,6,7] => ? = 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,2,6,3,4,8,5,7] => [1,2,6,3,4,5,7] => [1,2,3,6,4,5,7] => ? = 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,2,7,3,4,5,8,6] => [1,2,7,3,4,5,6] => [1,2,3,7,4,5,6] => ? = 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7] => [1,3,4,5,6,2,7] => ? = 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=> [1,3,2,4,5,8,6,7] => [1,3,2,4,5,6,7] => [1,3,4,5,6,2,7] => ? = 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,3,2,4,8,5,6,7] => [1,3,2,4,5,6,7] => [1,3,4,5,6,2,7] => ? = 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=> [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => ? = 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,5,4,8,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => ? = 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,3,2,5,8,4,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => ? = 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
=> [1,3,2,6,4,5,7,8] => [1,3,2,6,4,5,7] => [1,3,4,2,6,5,7] => ? = 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=> [1,3,2,6,4,8,5,7] => [1,3,2,6,4,5,7] => [1,3,4,2,6,5,7] => ? = 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> [1,3,2,7,4,5,6,8] => [1,3,2,7,4,5,6] => [1,3,4,2,7,5,6] => ? = 3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [1,3,2,7,4,8,5,6] => [1,3,2,7,4,5,6] => [1,3,4,2,7,5,6] => ? = 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,3,2,8,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,4,5,6,2,7] => ? = 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [1,3,4,2,8,5,6,7] => [1,3,4,2,5,6,7] => [1,3,4,5,2,6,7] => ? = 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [1,3,5,2,6,8,4,7] => [1,3,5,2,6,4,7] => [1,3,2,5,4,6,7] => ? = 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,3,5,8,2,4,6,7] => [1,3,5,2,4,6,7] => [1,3,5,6,2,4,7] => ? = 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [1,3,7,2,8,4,5,6] => [1,3,7,2,4,5,6] => [1,3,4,7,2,5,6] => ? = 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=> [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7] => [1,2,4,5,6,3,7] => ? = 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
=> [1,4,2,3,5,8,6,7] => [1,4,2,3,5,6,7] => [1,2,4,5,6,3,7] => ? = 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=> [1,4,2,3,7,5,6,8] => [1,4,2,3,7,5,6] => [1,4,2,3,7,5,6] => ? = 4
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [1,4,2,3,8,5,6,7] => [1,4,2,3,5,6,7] => [1,2,4,5,6,3,7] => ? = 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
=> [1,4,2,5,3,6,7,8] => [1,4,2,5,3,6,7] => [1,4,5,2,6,3,7] => ? = 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
=> [1,4,2,5,3,8,6,7] => [1,4,2,5,3,6,7] => [1,4,5,2,6,3,7] => ? = 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [1,4,2,5,8,3,6,7] => [1,4,2,5,3,6,7] => [1,4,5,2,6,3,7] => ? = 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
=> [1,4,2,6,3,5,7,8] => [1,4,2,6,3,5,7] => [1,2,4,3,6,5,7] => ? = 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=> [1,4,2,6,3,8,5,7] => [1,4,2,6,3,5,7] => [1,2,4,3,6,5,7] => ? = 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
=> [1,4,2,7,3,5,6,8] => [1,4,2,7,3,5,6] => [1,2,4,3,7,5,6] => ? = 3
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
=> [1,4,2,7,3,8,5,6] => [1,4,2,7,3,5,6] => [1,2,4,3,7,5,6] => ? = 3
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=> [1,4,2,7,8,3,5,6] => [1,4,2,7,3,5,6] => [1,2,4,3,7,5,6] => ? = 3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> [1,4,2,8,3,5,6,7] => [1,4,2,3,5,6,7] => [1,2,4,5,6,3,7] => ? = 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
=> [1,4,5,2,6,3,7,8] => [1,4,5,2,6,3,7] => [1,4,2,5,3,6,7] => ? = 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
=> [1,4,5,2,6,3,8,7] => [1,4,5,2,6,3,7] => [1,4,2,5,3,6,7] => ? = 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=> [1,4,7,8,2,3,5,6] => [1,4,7,2,3,5,6] => [1,2,4,7,3,5,6] => ? = 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
=> [1,5,2,3,4,6,7,8] => [1,5,2,3,4,6,7] => [1,2,3,5,6,4,7] => ? = 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> [1,5,2,3,4,8,6,7] => [1,5,2,3,4,6,7] => [1,2,3,5,6,4,7] => ? = 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
=> [1,5,2,6,3,4,7,8] => [1,5,2,6,3,4,7] => [1,2,5,3,6,4,7] => ? = 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=> [1,5,2,6,3,8,4,7] => [1,5,2,6,3,4,7] => [1,2,5,3,6,4,7] => ? = 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
=> [1,5,2,7,3,4,6,8] => [1,5,2,7,3,4,6] => [1,2,5,3,7,4,6] => ? = 3
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=> [1,5,2,7,3,8,4,6] => [1,5,2,7,3,4,6] => [1,2,5,3,7,4,6] => ? = 3
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,5,2,8,3,4,6,7] => [1,5,2,3,4,6,7] => [1,2,3,5,6,4,7] => ? = 1
Description
The lec statistic, the sum of the inversion numbers of the hook factors of a permutation.
For a permutation $\sigma = p \tau_{1} \tau_{2} \cdots \tau_{k}$ in its hook factorization, [1] defines $$ \textrm{lec} \, \sigma = \sum_{1 \leq i \leq k} \textrm{inv} \, \tau_{i} \, ,$$ where $\textrm{inv} \, \tau_{i}$ is the number of inversions of $\tau_{i}$.
Matching statistic: St000316
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St000316: Permutations ⟶ ℤResult quality: 67% ●values known / values provided: 67%●distinct values known / distinct values provided: 67%
Mp00252: Permutations —restriction⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St000316: Permutations ⟶ ℤResult quality: 67% ●values known / values provided: 67%●distinct values known / distinct values provided: 67%
Values
[1,0]
=> [1] => [] => [] => ? = 0
[1,0,1,0]
=> [1,2] => [1] => [1] => 0
[1,1,0,0]
=> [2,1] => [1] => [1] => 0
[1,0,1,0,1,0]
=> [1,2,3] => [1,2] => [1,2] => 0
[1,0,1,1,0,0]
=> [1,3,2] => [1,2] => [1,2] => 0
[1,1,0,0,1,0]
=> [2,1,3] => [2,1] => [2,1] => 1
[1,1,0,1,0,0]
=> [2,3,1] => [2,1] => [2,1] => 1
[1,1,1,0,0,0]
=> [3,1,2] => [1,2] => [1,2] => 0
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [1,3,2] => [3,1,2] => 2
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [1,3,2] => [3,1,2] => 2
[1,0,1,1,1,0,0,0]
=> [1,4,2,3] => [1,2,3] => [1,2,3] => 0
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,3] => [2,3,1] => 1
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,1,3] => [2,3,1] => 1
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => [2,3,1] => [2,1,3] => 1
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => [2,3,1] => [2,1,3] => 1
[1,1,0,1,1,0,0,0]
=> [2,4,1,3] => [2,1,3] => [2,3,1] => 1
[1,1,1,0,0,0,1,0]
=> [3,1,2,4] => [3,1,2] => [1,3,2] => 1
[1,1,1,0,0,1,0,0]
=> [3,1,4,2] => [3,1,2] => [1,3,2] => 1
[1,1,1,0,1,0,0,0]
=> [3,4,1,2] => [3,1,2] => [1,3,2] => 1
[1,1,1,1,0,0,0,0]
=> [4,1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [1,2,4,3] => [4,1,2,3] => 3
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [1,2,4,3] => [4,1,2,3] => 3
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [1,3,4,2] => [3,1,2,4] => 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [1,3,4,2] => [3,1,2,4] => 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,2,3,5] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,2,5,3] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,4,5,2,3] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,1,4,3] => [2,1,4,3] => 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [2,1,4,3] => [2,1,4,3] => 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,3,4] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [2,3,4,1] => [2,1,3,4] => 1
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [2,3,4,1] => [2,1,3,4] => 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => [2,3,1,4] => [2,3,1,4] => 1
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,5,3] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => [2,4,1,3] => [2,4,1,3] => 2
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,1,3,4] => [2,1,3,4] => [2,3,4,1] => 1
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,2,4,5] => [3,1,2,4] => [1,3,4,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => ? = 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,4,5,7,8,6] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => ? = 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,3,4,6,7,8,5] => [1,2,3,4,6,7,5] => [6,1,2,3,4,5,7] => ? = 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,2,3,4,7,5,8,6] => [1,2,3,4,7,5,6] => [1,7,2,3,4,5,6] => ? = 5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,2,3,4,7,8,5,6] => [1,2,3,4,7,5,6] => [1,7,2,3,4,5,6] => ? = 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,2,3,4,8,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7] => [1,2,5,3,4,6,7] => ? = 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,2,3,5,4,8,6,7] => [1,2,3,5,4,6,7] => [1,2,5,3,4,6,7] => ? = 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,2,3,5,6,7,8,4] => [1,2,3,5,6,7,4] => [5,1,2,3,4,6,7] => ? = 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7] => [1,2,6,3,4,5,7] => ? = 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,2,3,6,4,8,5,7] => [1,2,3,6,4,5,7] => [1,2,6,3,4,5,7] => ? = 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,2,3,6,7,4,8,5] => [1,2,3,6,7,4,5] => [6,7,1,2,3,4,5] => ? = 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ? = 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,2,3,7,4,5,8,6] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ? = 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,2,3,7,4,8,5,6] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => ? = 4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,8,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7] => [1,4,2,6,3,5,7] => ? = 3
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,2,4,3,8,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,5,3,6,7] => ? = 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,2,4,5,6,7,8,3] => [1,2,4,5,6,7,3] => [4,1,2,3,5,6,7] => ? = 3
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,2,4,6,7,8,3,5] => [1,2,4,6,7,3,5] => [4,6,1,2,3,5,7] => ? = 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=> [1,2,5,3,6,7,4,8] => [1,2,5,3,6,7,4] => [5,1,2,6,3,4,7] => ? = 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,2,5,3,6,7,8,4] => [1,2,5,3,6,7,4] => [5,1,2,6,3,4,7] => ? = 4
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,2,5,3,8,4,6,7] => [1,2,5,3,4,6,7] => [1,2,3,5,4,6,7] => ? = 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,2,5,6,3,7,8,4] => [1,2,5,6,3,7,4] => [5,1,6,2,3,4,7] => ? = 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,2,5,6,7,3,8,4] => [1,2,5,6,7,3,4] => [5,6,1,2,3,4,7] => ? = 4
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,2,5,6,7,8,3,4] => [1,2,5,6,7,3,4] => [5,6,1,2,3,4,7] => ? = 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,2,6,3,4,7,8,5] => [1,2,6,3,4,7,5] => [6,1,2,7,3,4,5] => ? = 5
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,2,6,3,4,8,5,7] => [1,2,6,3,4,5,7] => [1,2,3,6,4,5,7] => ? = 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,2,6,3,7,4,5,8] => [1,2,6,3,7,4,5] => [1,6,2,7,3,4,5] => ? = 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,2,7,3,4,5,8,6] => [1,2,7,3,4,5,6] => [1,2,3,7,4,5,6] => ? = 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7] => [1,3,4,5,6,2,7] => ? = 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=> [1,3,2,4,5,8,6,7] => [1,3,2,4,5,6,7] => [1,3,4,5,6,2,7] => ? = 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,3,2,4,8,5,6,7] => [1,3,2,4,5,6,7] => [1,3,4,5,6,2,7] => ? = 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=> [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => ? = 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,5,4,8,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => ? = 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,3,2,5,8,4,6,7] => [1,3,2,5,4,6,7] => [1,3,5,2,6,4,7] => ? = 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
=> [1,3,2,6,4,5,7,8] => [1,3,2,6,4,5,7] => [1,3,4,2,6,5,7] => ? = 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=> [1,3,2,6,4,8,5,7] => [1,3,2,6,4,5,7] => [1,3,4,2,6,5,7] => ? = 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> [1,3,2,7,4,5,6,8] => [1,3,2,7,4,5,6] => [1,3,4,2,7,5,6] => ? = 3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [1,3,2,7,4,8,5,6] => [1,3,2,7,4,5,6] => [1,3,4,2,7,5,6] => ? = 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,3,2,8,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,4,5,6,2,7] => ? = 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [1,3,4,2,8,5,6,7] => [1,3,4,2,5,6,7] => [1,3,4,5,2,6,7] => ? = 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,3,4,5,6,7,8,2] => [1,3,4,5,6,7,2] => [3,1,2,4,5,6,7] => ? = 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [1,3,4,6,7,2,8,5] => [1,3,4,6,7,2,5] => [3,6,1,2,4,5,7] => ? = 4
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [1,3,5,2,6,8,4,7] => [1,3,5,2,6,4,7] => [1,3,2,5,4,6,7] => ? = 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,3,5,8,2,4,6,7] => [1,3,5,2,4,6,7] => [1,3,5,6,2,4,7] => ? = 2
Description
The number of non-left-to-right-maxima of a permutation.
An integer $\sigma_i$ in the one-line notation of a permutation $\sigma$ is a **non-left-to-right-maximum** if there exists a $j < i$ such that $\sigma_j > \sigma_i$.
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!