Your data matches 40 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000938
Mp00253: Decorated permutations permutationPermutations
Mp00060: Permutations Robinson-Schensted tableau shapeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St000938: Integer partitions ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[3,+,1] => [3,2,1] => [1,1,1]
=> [1,1]
=> 0
[3,-,1] => [3,2,1] => [1,1,1]
=> [1,1]
=> 0
[+,4,+,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 0
[-,4,+,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 0
[+,4,-,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 0
[-,4,-,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 0
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 0
[2,4,1,3] => [2,4,1,3] => [2,2]
=> [2]
=> 0
[2,4,+,1] => [2,4,3,1] => [2,1,1]
=> [1,1]
=> 0
[2,4,-,1] => [2,4,3,1] => [2,1,1]
=> [1,1]
=> 0
[3,1,4,2] => [3,1,4,2] => [2,2]
=> [2]
=> 0
[3,+,1,+] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 0
[3,-,1,+] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 0
[3,+,1,-] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 0
[3,-,1,-] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 0
[3,+,4,1] => [3,2,4,1] => [2,1,1]
=> [1,1]
=> 0
[3,-,4,1] => [3,2,4,1] => [2,1,1]
=> [1,1]
=> 0
[3,4,1,2] => [3,4,1,2] => [2,2]
=> [2]
=> 0
[3,4,2,1] => [3,4,2,1] => [2,1,1]
=> [1,1]
=> 0
[4,1,+,2] => [4,1,3,2] => [2,1,1]
=> [1,1]
=> 0
[4,1,-,2] => [4,1,3,2] => [2,1,1]
=> [1,1]
=> 0
[4,+,1,3] => [4,2,1,3] => [2,1,1]
=> [1,1]
=> 0
[4,-,1,3] => [4,2,1,3] => [2,1,1]
=> [1,1]
=> 0
[4,+,+,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 0
[4,-,+,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 0
[4,+,-,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 0
[4,-,-,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 0
[4,3,1,2] => [4,3,1,2] => [2,1,1]
=> [1,1]
=> 0
[4,3,2,1] => [4,3,2,1] => [1,1,1,1]
=> [1,1,1]
=> 0
[+,+,5,+,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[-,+,5,+,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[+,-,5,+,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[+,+,5,-,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[-,-,5,+,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[-,+,5,-,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[+,-,5,-,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[-,-,5,-,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[+,3,2,5,4] => [1,3,2,5,4] => [3,2]
=> [2]
=> 0
[-,3,2,5,4] => [1,3,2,5,4] => [3,2]
=> [2]
=> 0
[+,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> 0
[-,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> 0
[+,3,5,+,2] => [1,3,5,4,2] => [3,1,1]
=> [1,1]
=> 0
[-,3,5,+,2] => [1,3,5,4,2] => [3,1,1]
=> [1,1]
=> 0
[+,3,5,-,2] => [1,3,5,4,2] => [3,1,1]
=> [1,1]
=> 0
[-,3,5,-,2] => [1,3,5,4,2] => [3,1,1]
=> [1,1]
=> 0
[+,4,2,5,3] => [1,4,2,5,3] => [3,2]
=> [2]
=> 0
[-,4,2,5,3] => [1,4,2,5,3] => [3,2]
=> [2]
=> 0
[+,4,+,2,+] => [1,4,3,2,5] => [3,1,1]
=> [1,1]
=> 0
[-,4,+,2,+] => [1,4,3,2,5] => [3,1,1]
=> [1,1]
=> 0
[+,4,-,2,+] => [1,4,3,2,5] => [3,1,1]
=> [1,1]
=> 0
Description
The number of zeros of the symmetric group character corresponding to the partition. For example, the character values of the irreducible representation $S^{(2,2)}$ are $2$ on the conjugacy classes $(4)$ and $(2,2)$, $0$ on the conjugacy classes $(3,1)$ and $(1,1,1,1)$, and $-1$ on the conjugacy class $(2,1,1)$. Therefore, the statistic on the partition $(2,2)$ is $2$.
Matching statistic: St001214
Mp00253: Decorated permutations permutationPermutations
Mp00060: Permutations Robinson-Schensted tableau shapeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001214: Integer partitions ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[3,+,1] => [3,2,1] => [1,1,1]
=> [1,1]
=> 0
[3,-,1] => [3,2,1] => [1,1,1]
=> [1,1]
=> 0
[+,4,+,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 0
[-,4,+,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 0
[+,4,-,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 0
[-,4,-,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 0
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 0
[2,4,1,3] => [2,4,1,3] => [2,2]
=> [2]
=> 0
[2,4,+,1] => [2,4,3,1] => [2,1,1]
=> [1,1]
=> 0
[2,4,-,1] => [2,4,3,1] => [2,1,1]
=> [1,1]
=> 0
[3,1,4,2] => [3,1,4,2] => [2,2]
=> [2]
=> 0
[3,+,1,+] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 0
[3,-,1,+] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 0
[3,+,1,-] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 0
[3,-,1,-] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 0
[3,+,4,1] => [3,2,4,1] => [2,1,1]
=> [1,1]
=> 0
[3,-,4,1] => [3,2,4,1] => [2,1,1]
=> [1,1]
=> 0
[3,4,1,2] => [3,4,1,2] => [2,2]
=> [2]
=> 0
[3,4,2,1] => [3,4,2,1] => [2,1,1]
=> [1,1]
=> 0
[4,1,+,2] => [4,1,3,2] => [2,1,1]
=> [1,1]
=> 0
[4,1,-,2] => [4,1,3,2] => [2,1,1]
=> [1,1]
=> 0
[4,+,1,3] => [4,2,1,3] => [2,1,1]
=> [1,1]
=> 0
[4,-,1,3] => [4,2,1,3] => [2,1,1]
=> [1,1]
=> 0
[4,+,+,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 0
[4,-,+,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 0
[4,+,-,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 0
[4,-,-,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 0
[4,3,1,2] => [4,3,1,2] => [2,1,1]
=> [1,1]
=> 0
[4,3,2,1] => [4,3,2,1] => [1,1,1,1]
=> [1,1,1]
=> 0
[+,+,5,+,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[-,+,5,+,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[+,-,5,+,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[+,+,5,-,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[-,-,5,+,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[-,+,5,-,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[+,-,5,-,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[-,-,5,-,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 0
[+,3,2,5,4] => [1,3,2,5,4] => [3,2]
=> [2]
=> 0
[-,3,2,5,4] => [1,3,2,5,4] => [3,2]
=> [2]
=> 0
[+,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> 0
[-,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> 0
[+,3,5,+,2] => [1,3,5,4,2] => [3,1,1]
=> [1,1]
=> 0
[-,3,5,+,2] => [1,3,5,4,2] => [3,1,1]
=> [1,1]
=> 0
[+,3,5,-,2] => [1,3,5,4,2] => [3,1,1]
=> [1,1]
=> 0
[-,3,5,-,2] => [1,3,5,4,2] => [3,1,1]
=> [1,1]
=> 0
[+,4,2,5,3] => [1,4,2,5,3] => [3,2]
=> [2]
=> 0
[-,4,2,5,3] => [1,4,2,5,3] => [3,2]
=> [2]
=> 0
[+,4,+,2,+] => [1,4,3,2,5] => [3,1,1]
=> [1,1]
=> 0
[-,4,+,2,+] => [1,4,3,2,5] => [3,1,1]
=> [1,1]
=> 0
[+,4,-,2,+] => [1,4,3,2,5] => [3,1,1]
=> [1,1]
=> 0
Description
The aft of an integer partition. The aft is the size of the partition minus the length of the first row or column, whichever is larger. See also [[St000784]].
Mp00253: Decorated permutations permutationPermutations
Mp00254: Permutations Inverse fireworks mapPermutations
Mp00170: Permutations to signed permutationSigned permutations
St001771: Signed permutations ⟶ ℤResult quality: 6% values known / values provided: 6%distinct values known / distinct values provided: 33%
Values
[3,+,1] => [3,2,1] => [3,2,1] => [3,2,1] => 0
[3,-,1] => [3,2,1] => [3,2,1] => [3,2,1] => 0
[+,4,+,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[-,4,+,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[+,4,-,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[-,4,-,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 0
[2,4,1,3] => [2,4,1,3] => [2,4,1,3] => [2,4,1,3] => 0
[2,4,+,1] => [2,4,3,1] => [1,4,3,2] => [1,4,3,2] => 0
[2,4,-,1] => [2,4,3,1] => [1,4,3,2] => [1,4,3,2] => 0
[3,1,4,2] => [3,1,4,2] => [2,1,4,3] => [2,1,4,3] => 0
[3,+,1,+] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[3,-,1,+] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[3,+,1,-] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[3,-,1,-] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[3,+,4,1] => [3,2,4,1] => [2,1,4,3] => [2,1,4,3] => 0
[3,-,4,1] => [3,2,4,1] => [2,1,4,3] => [2,1,4,3] => 0
[3,4,1,2] => [3,4,1,2] => [2,4,1,3] => [2,4,1,3] => 0
[3,4,2,1] => [3,4,2,1] => [1,4,3,2] => [1,4,3,2] => 0
[4,1,+,2] => [4,1,3,2] => [4,1,3,2] => [4,1,3,2] => 0
[4,1,-,2] => [4,1,3,2] => [4,1,3,2] => [4,1,3,2] => 0
[4,+,1,3] => [4,2,1,3] => [4,2,1,3] => [4,2,1,3] => 0
[4,-,1,3] => [4,2,1,3] => [4,2,1,3] => [4,2,1,3] => 0
[4,+,+,1] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 0
[4,-,+,1] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 0
[4,+,-,1] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 0
[4,-,-,1] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 0
[4,3,1,2] => [4,3,1,2] => [4,3,1,2] => [4,3,1,2] => 0
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 0
[+,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[+,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[-,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[+,3,5,+,2] => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,3,5,+,2] => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,3,5,-,2] => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,3,5,-,2] => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,4,2,5,3] => [1,4,2,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[-,4,2,5,3] => [1,4,2,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[+,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[-,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[+,4,-,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[2,1,+,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[2,1,-,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[2,1,4,3,+] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[2,1,4,3,-] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[2,1,4,5,3] => [2,1,4,5,3] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,3,4] => ? = 0
[2,1,5,+,3] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[2,1,5,-,3] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[2,4,1,3,+] => [2,4,1,3,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[2,4,1,3,-] => [2,4,1,3,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[2,5,1,3,4] => [2,5,1,3,4] => [2,5,1,3,4] => [2,5,1,3,4] => ? = 0
[2,5,1,+,3] => [2,5,1,4,3] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
[2,5,1,-,3] => [2,5,1,4,3] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
[2,5,4,1,3] => [2,5,4,1,3] => [2,5,4,1,3] => [2,5,4,1,3] => ? = 1
[3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => ? = 0
[3,1,4,2,+] => [3,1,4,2,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,1,4,2,-] => [3,1,4,2,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,1,4,5,2] => [3,1,4,5,2] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[3,1,5,2,4] => [3,1,5,2,4] => [3,1,5,2,4] => [3,1,5,2,4] => ? = 0
[3,1,5,+,2] => [3,1,5,4,2] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,1,5,-,2] => [3,1,5,4,2] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,+,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,-,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,+,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,+,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,-,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,-,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,+,1,-,-] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,-,1,-,-] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,+,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ? = 1
[3,-,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ? = 1
[3,+,4,1,+] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,-,4,1,+] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,+,4,1,-] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,-,4,1,-] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,+,4,5,1] => [3,2,4,5,1] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[3,-,4,5,1] => [3,2,4,5,1] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[3,+,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => ? = 1
[3,-,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => ? = 1
[3,+,5,+,1] => [3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,-,5,+,1] => [3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,+,5,-,1] => [3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,-,5,-,1] => [3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,4,1,2,+] => [3,4,1,2,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[3,4,1,2,-] => [3,4,1,2,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[3,5,1,2,4] => [3,5,1,2,4] => [3,5,1,2,4] => [3,5,1,2,4] => ? = 0
[3,5,1,+,2] => [3,5,1,4,2] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
[3,5,1,-,2] => [3,5,1,4,2] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
[3,5,2,1,4] => [3,5,2,1,4] => [3,5,2,1,4] => [3,5,2,1,4] => ? = 1
[3,5,2,+,1] => [3,5,2,4,1] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
Description
The number of occurrences of the signed pattern 1-2 in a signed permutation. This is the number of pairs $1\leq i < j\leq n$ such that $0 < \pi(i) < -\pi(j)$.
Mp00253: Decorated permutations permutationPermutations
Mp00254: Permutations Inverse fireworks mapPermutations
Mp00170: Permutations to signed permutationSigned permutations
St001870: Signed permutations ⟶ ℤResult quality: 6% values known / values provided: 6%distinct values known / distinct values provided: 33%
Values
[3,+,1] => [3,2,1] => [3,2,1] => [3,2,1] => 0
[3,-,1] => [3,2,1] => [3,2,1] => [3,2,1] => 0
[+,4,+,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[-,4,+,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[+,4,-,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[-,4,-,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 0
[2,4,1,3] => [2,4,1,3] => [2,4,1,3] => [2,4,1,3] => 0
[2,4,+,1] => [2,4,3,1] => [1,4,3,2] => [1,4,3,2] => 0
[2,4,-,1] => [2,4,3,1] => [1,4,3,2] => [1,4,3,2] => 0
[3,1,4,2] => [3,1,4,2] => [2,1,4,3] => [2,1,4,3] => 0
[3,+,1,+] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[3,-,1,+] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[3,+,1,-] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[3,-,1,-] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[3,+,4,1] => [3,2,4,1] => [2,1,4,3] => [2,1,4,3] => 0
[3,-,4,1] => [3,2,4,1] => [2,1,4,3] => [2,1,4,3] => 0
[3,4,1,2] => [3,4,1,2] => [2,4,1,3] => [2,4,1,3] => 0
[3,4,2,1] => [3,4,2,1] => [1,4,3,2] => [1,4,3,2] => 0
[4,1,+,2] => [4,1,3,2] => [4,1,3,2] => [4,1,3,2] => 0
[4,1,-,2] => [4,1,3,2] => [4,1,3,2] => [4,1,3,2] => 0
[4,+,1,3] => [4,2,1,3] => [4,2,1,3] => [4,2,1,3] => 0
[4,-,1,3] => [4,2,1,3] => [4,2,1,3] => [4,2,1,3] => 0
[4,+,+,1] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 0
[4,-,+,1] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 0
[4,+,-,1] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 0
[4,-,-,1] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 0
[4,3,1,2] => [4,3,1,2] => [4,3,1,2] => [4,3,1,2] => 0
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 0
[+,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[+,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[-,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[+,3,5,+,2] => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,3,5,+,2] => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,3,5,-,2] => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,3,5,-,2] => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,4,2,5,3] => [1,4,2,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[-,4,2,5,3] => [1,4,2,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[+,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[-,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[+,4,-,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[2,1,+,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[2,1,-,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[2,1,4,3,+] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[2,1,4,3,-] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[2,1,4,5,3] => [2,1,4,5,3] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,3,4] => ? = 0
[2,1,5,+,3] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[2,1,5,-,3] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[2,4,1,3,+] => [2,4,1,3,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[2,4,1,3,-] => [2,4,1,3,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[2,5,1,3,4] => [2,5,1,3,4] => [2,5,1,3,4] => [2,5,1,3,4] => ? = 0
[2,5,1,+,3] => [2,5,1,4,3] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
[2,5,1,-,3] => [2,5,1,4,3] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
[2,5,4,1,3] => [2,5,4,1,3] => [2,5,4,1,3] => [2,5,4,1,3] => ? = 1
[3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => ? = 0
[3,1,4,2,+] => [3,1,4,2,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,1,4,2,-] => [3,1,4,2,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,1,4,5,2] => [3,1,4,5,2] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[3,1,5,2,4] => [3,1,5,2,4] => [3,1,5,2,4] => [3,1,5,2,4] => ? = 0
[3,1,5,+,2] => [3,1,5,4,2] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,1,5,-,2] => [3,1,5,4,2] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,+,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,-,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,+,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,+,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,-,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,-,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,+,1,-,-] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,-,1,-,-] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,+,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ? = 1
[3,-,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ? = 1
[3,+,4,1,+] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,-,4,1,+] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,+,4,1,-] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,-,4,1,-] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,+,4,5,1] => [3,2,4,5,1] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[3,-,4,5,1] => [3,2,4,5,1] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[3,+,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => ? = 1
[3,-,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => ? = 1
[3,+,5,+,1] => [3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,-,5,+,1] => [3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,+,5,-,1] => [3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,-,5,-,1] => [3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,4,1,2,+] => [3,4,1,2,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[3,4,1,2,-] => [3,4,1,2,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[3,5,1,2,4] => [3,5,1,2,4] => [3,5,1,2,4] => [3,5,1,2,4] => ? = 0
[3,5,1,+,2] => [3,5,1,4,2] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
[3,5,1,-,2] => [3,5,1,4,2] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
[3,5,2,1,4] => [3,5,2,1,4] => [3,5,2,1,4] => [3,5,2,1,4] => ? = 1
[3,5,2,+,1] => [3,5,2,4,1] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
Description
The number of positive entries followed by a negative entry in a signed permutation. For a signed permutation $\pi\in\mathfrak H_n$, this is the number of positive entries followed by a negative entry in $\pi(-n),\dots,\pi(-1),\pi(1),\dots,\pi(n)$.
Mp00253: Decorated permutations permutationPermutations
Mp00254: Permutations Inverse fireworks mapPermutations
Mp00170: Permutations to signed permutationSigned permutations
St001895: Signed permutations ⟶ ℤResult quality: 6% values known / values provided: 6%distinct values known / distinct values provided: 33%
Values
[3,+,1] => [3,2,1] => [3,2,1] => [3,2,1] => 0
[3,-,1] => [3,2,1] => [3,2,1] => [3,2,1] => 0
[+,4,+,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[-,4,+,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[+,4,-,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[-,4,-,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 0
[2,4,1,3] => [2,4,1,3] => [2,4,1,3] => [2,4,1,3] => 0
[2,4,+,1] => [2,4,3,1] => [1,4,3,2] => [1,4,3,2] => 0
[2,4,-,1] => [2,4,3,1] => [1,4,3,2] => [1,4,3,2] => 0
[3,1,4,2] => [3,1,4,2] => [2,1,4,3] => [2,1,4,3] => 0
[3,+,1,+] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[3,-,1,+] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[3,+,1,-] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[3,-,1,-] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
[3,+,4,1] => [3,2,4,1] => [2,1,4,3] => [2,1,4,3] => 0
[3,-,4,1] => [3,2,4,1] => [2,1,4,3] => [2,1,4,3] => 0
[3,4,1,2] => [3,4,1,2] => [2,4,1,3] => [2,4,1,3] => 0
[3,4,2,1] => [3,4,2,1] => [1,4,3,2] => [1,4,3,2] => 0
[4,1,+,2] => [4,1,3,2] => [4,1,3,2] => [4,1,3,2] => 0
[4,1,-,2] => [4,1,3,2] => [4,1,3,2] => [4,1,3,2] => 0
[4,+,1,3] => [4,2,1,3] => [4,2,1,3] => [4,2,1,3] => 0
[4,-,1,3] => [4,2,1,3] => [4,2,1,3] => [4,2,1,3] => 0
[4,+,+,1] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 0
[4,-,+,1] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 0
[4,+,-,1] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 0
[4,-,-,1] => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 0
[4,3,1,2] => [4,3,1,2] => [4,3,1,2] => [4,3,1,2] => 0
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 0
[+,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[+,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[-,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => 0
[+,3,5,+,2] => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,3,5,+,2] => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,3,5,-,2] => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[-,3,5,-,2] => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
[+,4,2,5,3] => [1,4,2,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[-,4,2,5,3] => [1,4,2,5,3] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[+,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[-,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[+,4,-,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
[2,1,+,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[2,1,-,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[2,1,4,3,+] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[2,1,4,3,-] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[2,1,4,5,3] => [2,1,4,5,3] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,3,4] => ? = 0
[2,1,5,+,3] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[2,1,5,-,3] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[2,4,1,3,+] => [2,4,1,3,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[2,4,1,3,-] => [2,4,1,3,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[2,5,1,3,4] => [2,5,1,3,4] => [2,5,1,3,4] => [2,5,1,3,4] => ? = 0
[2,5,1,+,3] => [2,5,1,4,3] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
[2,5,1,-,3] => [2,5,1,4,3] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
[2,5,4,1,3] => [2,5,4,1,3] => [2,5,4,1,3] => [2,5,4,1,3] => ? = 1
[3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => ? = 0
[3,1,4,2,+] => [3,1,4,2,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,1,4,2,-] => [3,1,4,2,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,1,4,5,2] => [3,1,4,5,2] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[3,1,5,2,4] => [3,1,5,2,4] => [3,1,5,2,4] => [3,1,5,2,4] => ? = 0
[3,1,5,+,2] => [3,1,5,4,2] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,1,5,-,2] => [3,1,5,4,2] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,+,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,-,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,+,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,+,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,-,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,-,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,+,1,-,-] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,-,1,-,-] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
[3,+,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ? = 1
[3,-,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ? = 1
[3,+,4,1,+] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,-,4,1,+] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,+,4,1,-] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,-,4,1,-] => [3,2,4,1,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 0
[3,+,4,5,1] => [3,2,4,5,1] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[3,-,4,5,1] => [3,2,4,5,1] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 0
[3,+,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => ? = 1
[3,-,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4] => ? = 1
[3,+,5,+,1] => [3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,-,5,+,1] => [3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,+,5,-,1] => [3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,-,5,-,1] => [3,2,5,4,1] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
[3,4,1,2,+] => [3,4,1,2,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[3,4,1,2,-] => [3,4,1,2,5] => [2,4,1,3,5] => [2,4,1,3,5] => ? = 0
[3,5,1,2,4] => [3,5,1,2,4] => [3,5,1,2,4] => [3,5,1,2,4] => ? = 0
[3,5,1,+,2] => [3,5,1,4,2] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
[3,5,1,-,2] => [3,5,1,4,2] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
[3,5,2,1,4] => [3,5,2,1,4] => [3,5,2,1,4] => [3,5,2,1,4] => ? = 1
[3,5,2,+,1] => [3,5,2,4,1] => [2,5,1,4,3] => [2,5,1,4,3] => ? = 1
Description
The oddness of a signed permutation. The direct sum of two signed permutations $\sigma\in\mathfrak H_k$ and $\tau\in\mathfrak H_m$ is the signed permutation in $\mathfrak H_{k+m}$ obtained by concatenating $\sigma$ with the result of increasing the absolute value of every entry in $\tau$ by $k$. This statistic records the number of blocks with an odd number of signs in the direct sum decomposition of a signed permutation.
Mp00253: Decorated permutations permutationPermutations
Mp00209: Permutations pattern posetPosets
St000068: Posets ⟶ ℤResult quality: 6% values known / values provided: 6%distinct values known / distinct values provided: 33%
Values
[3,+,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[3,-,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[+,4,+,2] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1 = 0 + 1
[-,4,+,2] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1 = 0 + 1
[+,4,-,2] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1 = 0 + 1
[-,4,-,2] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1 = 0 + 1
[2,1,4,3] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 1 = 0 + 1
[2,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 0 + 1
[2,4,+,1] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 0 + 1
[2,4,-,1] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 0 + 1
[3,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
=> ? = 0 + 1
[3,+,1,+] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1 = 0 + 1
[3,-,1,+] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1 = 0 + 1
[3,+,1,-] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1 = 0 + 1
[3,-,1,-] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1 = 0 + 1
[3,+,4,1] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 0 + 1
[3,-,4,1] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 0 + 1
[3,4,1,2] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 1 = 0 + 1
[3,4,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1 = 0 + 1
[4,1,+,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 0 + 1
[4,1,-,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 0 + 1
[4,+,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 0 + 1
[4,-,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 0 + 1
[4,+,+,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 0 + 1
[4,-,+,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 0 + 1
[4,+,-,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 0 + 1
[4,-,-,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 0 + 1
[4,3,1,2] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1 = 0 + 1
[4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[+,+,5,+,3] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[-,+,5,+,3] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[+,-,5,+,3] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[+,+,5,-,3] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[-,-,5,+,3] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[-,+,5,-,3] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[+,-,5,-,3] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[-,-,5,-,3] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[+,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 0 + 1
[-,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 0 + 1
[+,3,5,2,4] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 0 + 1
[-,3,5,2,4] => [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 0 + 1
[+,3,5,+,2] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 0 + 1
[-,3,5,+,2] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 0 + 1
[+,3,5,-,2] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 0 + 1
[-,3,5,-,2] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 0 + 1
[+,4,2,5,3] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 0 + 1
[-,4,2,5,3] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 0 + 1
[+,4,+,2,+] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0 + 1
[-,4,+,2,+] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0 + 1
[+,4,-,2,+] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0 + 1
[+,4,+,2,-] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0 + 1
[-,4,-,2,+] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0 + 1
[-,4,+,2,-] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0 + 1
[+,4,-,2,-] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0 + 1
[-,4,-,2,-] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0 + 1
[+,4,+,5,2] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[-,4,+,5,2] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[+,4,-,5,2] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[-,4,-,5,2] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[+,4,5,2,3] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 0 + 1
[-,4,5,2,3] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 0 + 1
[+,4,5,3,2] => [1,4,5,3,2] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0 + 1
[-,4,5,3,2] => [1,4,5,3,2] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0 + 1
[+,5,2,+,3] => [1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 0 + 1
[-,5,2,+,3] => [1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 0 + 1
[+,5,2,-,3] => [1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 0 + 1
[-,5,2,-,3] => [1,5,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 0 + 1
[+,5,+,2,4] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[-,5,+,2,4] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[+,5,-,2,4] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[-,5,-,2,4] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[+,5,+,+,2] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[-,5,+,+,2] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[+,5,-,+,2] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[+,5,+,-,2] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[-,5,-,+,2] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[-,5,+,-,2] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[+,5,-,-,2] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[-,5,-,-,2] => [1,5,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 0 + 1
[+,5,4,2,3] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0 + 1
[-,5,4,2,3] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 0 + 1
[+,5,4,3,2] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 1 = 0 + 1
[-,5,4,3,2] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 1 = 0 + 1
[2,1,+,5,4] => [2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 0 + 1
[2,1,-,5,4] => [2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 0 + 1
[2,1,4,3,+] => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 0 + 1
[2,1,4,3,-] => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 0 + 1
[3,+,1,+,+] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[3,-,1,+,+] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[3,+,1,-,+] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[3,+,1,+,-] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[3,-,1,-,+] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[3,-,1,+,-] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[3,+,1,-,-] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[3,-,1,-,-] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[3,4,5,2,1] => [3,4,5,2,1] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 1 = 0 + 1
[4,3,2,1,+] => [4,3,2,1,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 1 = 0 + 1
[4,3,2,1,-] => [4,3,2,1,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 1 = 0 + 1
[4,5,+,2,1] => [4,5,3,2,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 1 = 0 + 1
[4,5,-,2,1] => [4,5,3,2,1] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 1 = 0 + 1
Description
The number of minimal elements in a poset.
Matching statistic: St001772
Mp00253: Decorated permutations permutationPermutations
Mp00170: Permutations to signed permutationSigned permutations
Mp00244: Signed permutations barSigned permutations
St001772: Signed permutations ⟶ ℤResult quality: 4% values known / values provided: 4%distinct values known / distinct values provided: 33%
Values
[3,+,1] => [3,2,1] => [3,2,1] => [-3,-2,-1] => 0
[3,-,1] => [3,2,1] => [3,2,1] => [-3,-2,-1] => 0
[+,4,+,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[-,4,+,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[+,4,-,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[-,4,-,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [-2,-1,-4,-3] => 0
[2,4,1,3] => [2,4,1,3] => [2,4,1,3] => [-2,-4,-1,-3] => 0
[2,4,+,1] => [2,4,3,1] => [2,4,3,1] => [-2,-4,-3,-1] => 0
[2,4,-,1] => [2,4,3,1] => [2,4,3,1] => [-2,-4,-3,-1] => 0
[3,1,4,2] => [3,1,4,2] => [3,1,4,2] => [-3,-1,-4,-2] => 0
[3,+,1,+] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,-,1,+] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,+,1,-] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,-,1,-] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,+,4,1] => [3,2,4,1] => [3,2,4,1] => [-3,-2,-4,-1] => 0
[3,-,4,1] => [3,2,4,1] => [3,2,4,1] => [-3,-2,-4,-1] => 0
[3,4,1,2] => [3,4,1,2] => [3,4,1,2] => [-3,-4,-1,-2] => 0
[3,4,2,1] => [3,4,2,1] => [3,4,2,1] => [-3,-4,-2,-1] => 0
[4,1,+,2] => [4,1,3,2] => [4,1,3,2] => [-4,-1,-3,-2] => 0
[4,1,-,2] => [4,1,3,2] => [4,1,3,2] => [-4,-1,-3,-2] => 0
[4,+,1,3] => [4,2,1,3] => [4,2,1,3] => [-4,-2,-1,-3] => 0
[4,-,1,3] => [4,2,1,3] => [4,2,1,3] => [-4,-2,-1,-3] => 0
[4,+,+,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,-,+,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,+,-,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,-,-,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,3,1,2] => [4,3,1,2] => [4,3,1,2] => [-4,-3,-1,-2] => 0
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [-4,-3,-2,-1] => 0
[+,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [-1,-3,-2,-5,-4] => 0
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [-1,-3,-2,-5,-4] => 0
[+,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [-1,-3,-5,-2,-4] => 0
[-,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [-1,-3,-5,-2,-4] => 0
[+,3,5,+,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[-,3,5,+,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[+,3,5,-,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[-,3,5,-,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[+,4,2,5,3] => [1,4,2,5,3] => [1,4,2,5,3] => [-1,-4,-2,-5,-3] => 0
[-,4,2,5,3] => [1,4,2,5,3] => [1,4,2,5,3] => [-1,-4,-2,-5,-3] => 0
[+,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 0
[-,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 0
[+,4,-,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 0
[+,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [-1,-5,-4,-3,-2] => ? = 0
[-,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [-1,-5,-4,-3,-2] => ? = 0
[2,1,+,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [-2,-1,-3,-5,-4] => ? = 0
[2,1,-,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [-2,-1,-3,-5,-4] => ? = 0
[2,1,4,3,+] => [2,1,4,3,5] => [2,1,4,3,5] => [-2,-1,-4,-3,-5] => ? = 0
[2,1,4,3,-] => [2,1,4,3,5] => [2,1,4,3,5] => [-2,-1,-4,-3,-5] => ? = 0
[2,1,4,5,3] => [2,1,4,5,3] => [2,1,4,5,3] => [-2,-1,-4,-5,-3] => ? = 0
[2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,3,4] => [-2,-1,-5,-3,-4] => ? = 0
[2,1,5,+,3] => [2,1,5,4,3] => [2,1,5,4,3] => [-2,-1,-5,-4,-3] => ? = 1
[2,1,5,-,3] => [2,1,5,4,3] => [2,1,5,4,3] => [-2,-1,-5,-4,-3] => ? = 1
[2,3,1,5,4] => [2,3,1,5,4] => [2,3,1,5,4] => [-2,-3,-1,-5,-4] => ? = 0
[2,3,5,1,4] => [2,3,5,1,4] => [2,3,5,1,4] => [-2,-3,-5,-1,-4] => ? = 0
[2,3,5,+,1] => [2,3,5,4,1] => [2,3,5,4,1] => [-2,-3,-5,-4,-1] => ? = 0
[2,3,5,-,1] => [2,3,5,4,1] => [2,3,5,4,1] => [-2,-3,-5,-4,-1] => ? = 0
[2,4,1,3,+] => [2,4,1,3,5] => [2,4,1,3,5] => [-2,-4,-1,-3,-5] => ? = 0
[2,4,1,3,-] => [2,4,1,3,5] => [2,4,1,3,5] => [-2,-4,-1,-3,-5] => ? = 0
[2,4,1,5,3] => [2,4,1,5,3] => [2,4,1,5,3] => [-2,-4,-1,-5,-3] => ? = 0
[2,4,+,1,+] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,-,1,+] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,+,1,-] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,-,1,-] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,+,5,1] => [2,4,3,5,1] => [2,4,3,5,1] => [-2,-4,-3,-5,-1] => ? = 0
[2,4,-,5,1] => [2,4,3,5,1] => [2,4,3,5,1] => [-2,-4,-3,-5,-1] => ? = 0
[2,4,5,1,3] => [2,4,5,1,3] => [2,4,5,1,3] => [-2,-4,-5,-1,-3] => ? = 0
[2,4,5,3,1] => [2,4,5,3,1] => [2,4,5,3,1] => [-2,-4,-5,-3,-1] => ? = 0
[2,5,1,3,4] => [2,5,1,3,4] => [2,5,1,3,4] => [-2,-5,-1,-3,-4] => ? = 0
[2,5,1,+,3] => [2,5,1,4,3] => [2,5,1,4,3] => [-2,-5,-1,-4,-3] => ? = 1
[2,5,1,-,3] => [2,5,1,4,3] => [2,5,1,4,3] => [-2,-5,-1,-4,-3] => ? = 1
[2,5,+,1,4] => [2,5,3,1,4] => [2,5,3,1,4] => [-2,-5,-3,-1,-4] => ? = 0
[2,5,-,1,4] => [2,5,3,1,4] => [2,5,3,1,4] => [-2,-5,-3,-1,-4] => ? = 0
[2,5,+,+,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,-,+,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,+,-,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,-,-,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,4,1,3] => [2,5,4,1,3] => [2,5,4,1,3] => [-2,-5,-4,-1,-3] => ? = 1
[2,5,4,3,1] => [2,5,4,3,1] => [2,5,4,3,1] => [-2,-5,-4,-3,-1] => ? = 0
[3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => [-3,-1,-2,-5,-4] => ? = 0
[3,1,4,2,+] => [3,1,4,2,5] => [3,1,4,2,5] => [-3,-1,-4,-2,-5] => ? = 0
[3,1,4,2,-] => [3,1,4,2,5] => [3,1,4,2,5] => [-3,-1,-4,-2,-5] => ? = 0
[3,1,4,5,2] => [3,1,4,5,2] => [3,1,4,5,2] => [-3,-1,-4,-5,-2] => ? = 0
[3,1,5,2,4] => [3,1,5,2,4] => [3,1,5,2,4] => [-3,-1,-5,-2,-4] => ? = 0
[3,1,5,+,2] => [3,1,5,4,2] => [3,1,5,4,2] => [-3,-1,-5,-4,-2] => ? = 1
[3,1,5,-,2] => [3,1,5,4,2] => [3,1,5,4,2] => [-3,-1,-5,-4,-2] => ? = 1
[3,+,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,-,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,+,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,+,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,-,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,-,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,+,1,-,-] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
Description
The number of occurrences of the signed pattern 12 in a signed permutation. This is the number of pairs $1\leq i < j\leq n$ such that $0 < \pi(i) < \pi(j)$.
Matching statistic: St001863
Mp00253: Decorated permutations permutationPermutations
Mp00170: Permutations to signed permutationSigned permutations
Mp00244: Signed permutations barSigned permutations
St001863: Signed permutations ⟶ ℤResult quality: 4% values known / values provided: 4%distinct values known / distinct values provided: 33%
Values
[3,+,1] => [3,2,1] => [3,2,1] => [-3,-2,-1] => 0
[3,-,1] => [3,2,1] => [3,2,1] => [-3,-2,-1] => 0
[+,4,+,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[-,4,+,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[+,4,-,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[-,4,-,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [-2,-1,-4,-3] => 0
[2,4,1,3] => [2,4,1,3] => [2,4,1,3] => [-2,-4,-1,-3] => 0
[2,4,+,1] => [2,4,3,1] => [2,4,3,1] => [-2,-4,-3,-1] => 0
[2,4,-,1] => [2,4,3,1] => [2,4,3,1] => [-2,-4,-3,-1] => 0
[3,1,4,2] => [3,1,4,2] => [3,1,4,2] => [-3,-1,-4,-2] => 0
[3,+,1,+] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,-,1,+] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,+,1,-] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,-,1,-] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,+,4,1] => [3,2,4,1] => [3,2,4,1] => [-3,-2,-4,-1] => 0
[3,-,4,1] => [3,2,4,1] => [3,2,4,1] => [-3,-2,-4,-1] => 0
[3,4,1,2] => [3,4,1,2] => [3,4,1,2] => [-3,-4,-1,-2] => 0
[3,4,2,1] => [3,4,2,1] => [3,4,2,1] => [-3,-4,-2,-1] => 0
[4,1,+,2] => [4,1,3,2] => [4,1,3,2] => [-4,-1,-3,-2] => 0
[4,1,-,2] => [4,1,3,2] => [4,1,3,2] => [-4,-1,-3,-2] => 0
[4,+,1,3] => [4,2,1,3] => [4,2,1,3] => [-4,-2,-1,-3] => 0
[4,-,1,3] => [4,2,1,3] => [4,2,1,3] => [-4,-2,-1,-3] => 0
[4,+,+,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,-,+,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,+,-,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,-,-,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,3,1,2] => [4,3,1,2] => [4,3,1,2] => [-4,-3,-1,-2] => 0
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [-4,-3,-2,-1] => 0
[+,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [-1,-3,-2,-5,-4] => 0
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [-1,-3,-2,-5,-4] => 0
[+,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [-1,-3,-5,-2,-4] => 0
[-,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [-1,-3,-5,-2,-4] => 0
[+,3,5,+,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[-,3,5,+,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[+,3,5,-,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[-,3,5,-,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[+,4,2,5,3] => [1,4,2,5,3] => [1,4,2,5,3] => [-1,-4,-2,-5,-3] => 0
[-,4,2,5,3] => [1,4,2,5,3] => [1,4,2,5,3] => [-1,-4,-2,-5,-3] => 0
[+,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 0
[-,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 0
[+,4,-,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 0
[+,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [-1,-5,-4,-3,-2] => ? = 0
[-,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [-1,-5,-4,-3,-2] => ? = 0
[2,1,+,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [-2,-1,-3,-5,-4] => ? = 0
[2,1,-,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [-2,-1,-3,-5,-4] => ? = 0
[2,1,4,3,+] => [2,1,4,3,5] => [2,1,4,3,5] => [-2,-1,-4,-3,-5] => ? = 0
[2,1,4,3,-] => [2,1,4,3,5] => [2,1,4,3,5] => [-2,-1,-4,-3,-5] => ? = 0
[2,1,4,5,3] => [2,1,4,5,3] => [2,1,4,5,3] => [-2,-1,-4,-5,-3] => ? = 0
[2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,3,4] => [-2,-1,-5,-3,-4] => ? = 0
[2,1,5,+,3] => [2,1,5,4,3] => [2,1,5,4,3] => [-2,-1,-5,-4,-3] => ? = 1
[2,1,5,-,3] => [2,1,5,4,3] => [2,1,5,4,3] => [-2,-1,-5,-4,-3] => ? = 1
[2,3,1,5,4] => [2,3,1,5,4] => [2,3,1,5,4] => [-2,-3,-1,-5,-4] => ? = 0
[2,3,5,1,4] => [2,3,5,1,4] => [2,3,5,1,4] => [-2,-3,-5,-1,-4] => ? = 0
[2,3,5,+,1] => [2,3,5,4,1] => [2,3,5,4,1] => [-2,-3,-5,-4,-1] => ? = 0
[2,3,5,-,1] => [2,3,5,4,1] => [2,3,5,4,1] => [-2,-3,-5,-4,-1] => ? = 0
[2,4,1,3,+] => [2,4,1,3,5] => [2,4,1,3,5] => [-2,-4,-1,-3,-5] => ? = 0
[2,4,1,3,-] => [2,4,1,3,5] => [2,4,1,3,5] => [-2,-4,-1,-3,-5] => ? = 0
[2,4,1,5,3] => [2,4,1,5,3] => [2,4,1,5,3] => [-2,-4,-1,-5,-3] => ? = 0
[2,4,+,1,+] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,-,1,+] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,+,1,-] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,-,1,-] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,+,5,1] => [2,4,3,5,1] => [2,4,3,5,1] => [-2,-4,-3,-5,-1] => ? = 0
[2,4,-,5,1] => [2,4,3,5,1] => [2,4,3,5,1] => [-2,-4,-3,-5,-1] => ? = 0
[2,4,5,1,3] => [2,4,5,1,3] => [2,4,5,1,3] => [-2,-4,-5,-1,-3] => ? = 0
[2,4,5,3,1] => [2,4,5,3,1] => [2,4,5,3,1] => [-2,-4,-5,-3,-1] => ? = 0
[2,5,1,3,4] => [2,5,1,3,4] => [2,5,1,3,4] => [-2,-5,-1,-3,-4] => ? = 0
[2,5,1,+,3] => [2,5,1,4,3] => [2,5,1,4,3] => [-2,-5,-1,-4,-3] => ? = 1
[2,5,1,-,3] => [2,5,1,4,3] => [2,5,1,4,3] => [-2,-5,-1,-4,-3] => ? = 1
[2,5,+,1,4] => [2,5,3,1,4] => [2,5,3,1,4] => [-2,-5,-3,-1,-4] => ? = 0
[2,5,-,1,4] => [2,5,3,1,4] => [2,5,3,1,4] => [-2,-5,-3,-1,-4] => ? = 0
[2,5,+,+,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,-,+,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,+,-,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,-,-,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,4,1,3] => [2,5,4,1,3] => [2,5,4,1,3] => [-2,-5,-4,-1,-3] => ? = 1
[2,5,4,3,1] => [2,5,4,3,1] => [2,5,4,3,1] => [-2,-5,-4,-3,-1] => ? = 0
[3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => [-3,-1,-2,-5,-4] => ? = 0
[3,1,4,2,+] => [3,1,4,2,5] => [3,1,4,2,5] => [-3,-1,-4,-2,-5] => ? = 0
[3,1,4,2,-] => [3,1,4,2,5] => [3,1,4,2,5] => [-3,-1,-4,-2,-5] => ? = 0
[3,1,4,5,2] => [3,1,4,5,2] => [3,1,4,5,2] => [-3,-1,-4,-5,-2] => ? = 0
[3,1,5,2,4] => [3,1,5,2,4] => [3,1,5,2,4] => [-3,-1,-5,-2,-4] => ? = 0
[3,1,5,+,2] => [3,1,5,4,2] => [3,1,5,4,2] => [-3,-1,-5,-4,-2] => ? = 1
[3,1,5,-,2] => [3,1,5,4,2] => [3,1,5,4,2] => [-3,-1,-5,-4,-2] => ? = 1
[3,+,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,-,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,+,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,+,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,-,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,-,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,+,1,-,-] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
Description
The number of weak excedances of a signed permutation. For a signed permutation $\pi\in\mathfrak H_n$, this is $\lvert\{i\in[n] \mid \pi(i) \geq i\}\rvert$.
Mp00253: Decorated permutations permutationPermutations
Mp00170: Permutations to signed permutationSigned permutations
Mp00244: Signed permutations barSigned permutations
St001864: Signed permutations ⟶ ℤResult quality: 4% values known / values provided: 4%distinct values known / distinct values provided: 33%
Values
[3,+,1] => [3,2,1] => [3,2,1] => [-3,-2,-1] => 0
[3,-,1] => [3,2,1] => [3,2,1] => [-3,-2,-1] => 0
[+,4,+,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[-,4,+,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[+,4,-,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[-,4,-,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [-2,-1,-4,-3] => 0
[2,4,1,3] => [2,4,1,3] => [2,4,1,3] => [-2,-4,-1,-3] => 0
[2,4,+,1] => [2,4,3,1] => [2,4,3,1] => [-2,-4,-3,-1] => 0
[2,4,-,1] => [2,4,3,1] => [2,4,3,1] => [-2,-4,-3,-1] => 0
[3,1,4,2] => [3,1,4,2] => [3,1,4,2] => [-3,-1,-4,-2] => 0
[3,+,1,+] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,-,1,+] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,+,1,-] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,-,1,-] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,+,4,1] => [3,2,4,1] => [3,2,4,1] => [-3,-2,-4,-1] => 0
[3,-,4,1] => [3,2,4,1] => [3,2,4,1] => [-3,-2,-4,-1] => 0
[3,4,1,2] => [3,4,1,2] => [3,4,1,2] => [-3,-4,-1,-2] => 0
[3,4,2,1] => [3,4,2,1] => [3,4,2,1] => [-3,-4,-2,-1] => 0
[4,1,+,2] => [4,1,3,2] => [4,1,3,2] => [-4,-1,-3,-2] => 0
[4,1,-,2] => [4,1,3,2] => [4,1,3,2] => [-4,-1,-3,-2] => 0
[4,+,1,3] => [4,2,1,3] => [4,2,1,3] => [-4,-2,-1,-3] => 0
[4,-,1,3] => [4,2,1,3] => [4,2,1,3] => [-4,-2,-1,-3] => 0
[4,+,+,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,-,+,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,+,-,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,-,-,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,3,1,2] => [4,3,1,2] => [4,3,1,2] => [-4,-3,-1,-2] => 0
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [-4,-3,-2,-1] => 0
[+,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [-1,-3,-2,-5,-4] => 0
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [-1,-3,-2,-5,-4] => 0
[+,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [-1,-3,-5,-2,-4] => 0
[-,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [-1,-3,-5,-2,-4] => 0
[+,3,5,+,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[-,3,5,+,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[+,3,5,-,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[-,3,5,-,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[+,4,2,5,3] => [1,4,2,5,3] => [1,4,2,5,3] => [-1,-4,-2,-5,-3] => 0
[-,4,2,5,3] => [1,4,2,5,3] => [1,4,2,5,3] => [-1,-4,-2,-5,-3] => 0
[+,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 0
[-,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 0
[+,4,-,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 0
[+,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [-1,-5,-4,-3,-2] => ? = 0
[-,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [-1,-5,-4,-3,-2] => ? = 0
[2,1,+,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [-2,-1,-3,-5,-4] => ? = 0
[2,1,-,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [-2,-1,-3,-5,-4] => ? = 0
[2,1,4,3,+] => [2,1,4,3,5] => [2,1,4,3,5] => [-2,-1,-4,-3,-5] => ? = 0
[2,1,4,3,-] => [2,1,4,3,5] => [2,1,4,3,5] => [-2,-1,-4,-3,-5] => ? = 0
[2,1,4,5,3] => [2,1,4,5,3] => [2,1,4,5,3] => [-2,-1,-4,-5,-3] => ? = 0
[2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,3,4] => [-2,-1,-5,-3,-4] => ? = 0
[2,1,5,+,3] => [2,1,5,4,3] => [2,1,5,4,3] => [-2,-1,-5,-4,-3] => ? = 1
[2,1,5,-,3] => [2,1,5,4,3] => [2,1,5,4,3] => [-2,-1,-5,-4,-3] => ? = 1
[2,3,1,5,4] => [2,3,1,5,4] => [2,3,1,5,4] => [-2,-3,-1,-5,-4] => ? = 0
[2,3,5,1,4] => [2,3,5,1,4] => [2,3,5,1,4] => [-2,-3,-5,-1,-4] => ? = 0
[2,3,5,+,1] => [2,3,5,4,1] => [2,3,5,4,1] => [-2,-3,-5,-4,-1] => ? = 0
[2,3,5,-,1] => [2,3,5,4,1] => [2,3,5,4,1] => [-2,-3,-5,-4,-1] => ? = 0
[2,4,1,3,+] => [2,4,1,3,5] => [2,4,1,3,5] => [-2,-4,-1,-3,-5] => ? = 0
[2,4,1,3,-] => [2,4,1,3,5] => [2,4,1,3,5] => [-2,-4,-1,-3,-5] => ? = 0
[2,4,1,5,3] => [2,4,1,5,3] => [2,4,1,5,3] => [-2,-4,-1,-5,-3] => ? = 0
[2,4,+,1,+] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,-,1,+] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,+,1,-] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,-,1,-] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,+,5,1] => [2,4,3,5,1] => [2,4,3,5,1] => [-2,-4,-3,-5,-1] => ? = 0
[2,4,-,5,1] => [2,4,3,5,1] => [2,4,3,5,1] => [-2,-4,-3,-5,-1] => ? = 0
[2,4,5,1,3] => [2,4,5,1,3] => [2,4,5,1,3] => [-2,-4,-5,-1,-3] => ? = 0
[2,4,5,3,1] => [2,4,5,3,1] => [2,4,5,3,1] => [-2,-4,-5,-3,-1] => ? = 0
[2,5,1,3,4] => [2,5,1,3,4] => [2,5,1,3,4] => [-2,-5,-1,-3,-4] => ? = 0
[2,5,1,+,3] => [2,5,1,4,3] => [2,5,1,4,3] => [-2,-5,-1,-4,-3] => ? = 1
[2,5,1,-,3] => [2,5,1,4,3] => [2,5,1,4,3] => [-2,-5,-1,-4,-3] => ? = 1
[2,5,+,1,4] => [2,5,3,1,4] => [2,5,3,1,4] => [-2,-5,-3,-1,-4] => ? = 0
[2,5,-,1,4] => [2,5,3,1,4] => [2,5,3,1,4] => [-2,-5,-3,-1,-4] => ? = 0
[2,5,+,+,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,-,+,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,+,-,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,-,-,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,4,1,3] => [2,5,4,1,3] => [2,5,4,1,3] => [-2,-5,-4,-1,-3] => ? = 1
[2,5,4,3,1] => [2,5,4,3,1] => [2,5,4,3,1] => [-2,-5,-4,-3,-1] => ? = 0
[3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => [-3,-1,-2,-5,-4] => ? = 0
[3,1,4,2,+] => [3,1,4,2,5] => [3,1,4,2,5] => [-3,-1,-4,-2,-5] => ? = 0
[3,1,4,2,-] => [3,1,4,2,5] => [3,1,4,2,5] => [-3,-1,-4,-2,-5] => ? = 0
[3,1,4,5,2] => [3,1,4,5,2] => [3,1,4,5,2] => [-3,-1,-4,-5,-2] => ? = 0
[3,1,5,2,4] => [3,1,5,2,4] => [3,1,5,2,4] => [-3,-1,-5,-2,-4] => ? = 0
[3,1,5,+,2] => [3,1,5,4,2] => [3,1,5,4,2] => [-3,-1,-5,-4,-2] => ? = 1
[3,1,5,-,2] => [3,1,5,4,2] => [3,1,5,4,2] => [-3,-1,-5,-4,-2] => ? = 1
[3,+,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,-,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,+,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,+,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,-,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,-,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,+,1,-,-] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
Description
The number of excedances of a signed permutation. For a signed permutation $\pi\in\mathfrak H_n$, this is $\lvert\{i\in[n] \mid \pi(i) > i\}\rvert$.
Matching statistic: St001867
Mp00253: Decorated permutations permutationPermutations
Mp00170: Permutations to signed permutationSigned permutations
Mp00244: Signed permutations barSigned permutations
St001867: Signed permutations ⟶ ℤResult quality: 4% values known / values provided: 4%distinct values known / distinct values provided: 33%
Values
[3,+,1] => [3,2,1] => [3,2,1] => [-3,-2,-1] => 0
[3,-,1] => [3,2,1] => [3,2,1] => [-3,-2,-1] => 0
[+,4,+,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[-,4,+,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[+,4,-,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[-,4,-,2] => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 0
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [-2,-1,-4,-3] => 0
[2,4,1,3] => [2,4,1,3] => [2,4,1,3] => [-2,-4,-1,-3] => 0
[2,4,+,1] => [2,4,3,1] => [2,4,3,1] => [-2,-4,-3,-1] => 0
[2,4,-,1] => [2,4,3,1] => [2,4,3,1] => [-2,-4,-3,-1] => 0
[3,1,4,2] => [3,1,4,2] => [3,1,4,2] => [-3,-1,-4,-2] => 0
[3,+,1,+] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,-,1,+] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,+,1,-] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,-,1,-] => [3,2,1,4] => [3,2,1,4] => [-3,-2,-1,-4] => 0
[3,+,4,1] => [3,2,4,1] => [3,2,4,1] => [-3,-2,-4,-1] => 0
[3,-,4,1] => [3,2,4,1] => [3,2,4,1] => [-3,-2,-4,-1] => 0
[3,4,1,2] => [3,4,1,2] => [3,4,1,2] => [-3,-4,-1,-2] => 0
[3,4,2,1] => [3,4,2,1] => [3,4,2,1] => [-3,-4,-2,-1] => 0
[4,1,+,2] => [4,1,3,2] => [4,1,3,2] => [-4,-1,-3,-2] => 0
[4,1,-,2] => [4,1,3,2] => [4,1,3,2] => [-4,-1,-3,-2] => 0
[4,+,1,3] => [4,2,1,3] => [4,2,1,3] => [-4,-2,-1,-3] => 0
[4,-,1,3] => [4,2,1,3] => [4,2,1,3] => [-4,-2,-1,-3] => 0
[4,+,+,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,-,+,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,+,-,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,-,-,1] => [4,2,3,1] => [4,2,3,1] => [-4,-2,-3,-1] => 0
[4,3,1,2] => [4,3,1,2] => [4,3,1,2] => [-4,-3,-1,-2] => 0
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [-4,-3,-2,-1] => 0
[+,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,+,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,-,5,+,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,+,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[-,-,5,-,3] => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 0
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [-1,-3,-2,-5,-4] => 0
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [-1,-3,-2,-5,-4] => 0
[+,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [-1,-3,-5,-2,-4] => 0
[-,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => [-1,-3,-5,-2,-4] => 0
[+,3,5,+,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[-,3,5,+,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[+,3,5,-,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[-,3,5,-,2] => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 0
[+,4,2,5,3] => [1,4,2,5,3] => [1,4,2,5,3] => [-1,-4,-2,-5,-3] => 0
[-,4,2,5,3] => [1,4,2,5,3] => [1,4,2,5,3] => [-1,-4,-2,-5,-3] => 0
[+,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 0
[-,4,+,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 0
[+,4,-,2,+] => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 0
[+,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [-1,-5,-4,-3,-2] => ? = 0
[-,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [-1,-5,-4,-3,-2] => ? = 0
[2,1,+,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [-2,-1,-3,-5,-4] => ? = 0
[2,1,-,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [-2,-1,-3,-5,-4] => ? = 0
[2,1,4,3,+] => [2,1,4,3,5] => [2,1,4,3,5] => [-2,-1,-4,-3,-5] => ? = 0
[2,1,4,3,-] => [2,1,4,3,5] => [2,1,4,3,5] => [-2,-1,-4,-3,-5] => ? = 0
[2,1,4,5,3] => [2,1,4,5,3] => [2,1,4,5,3] => [-2,-1,-4,-5,-3] => ? = 0
[2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,3,4] => [-2,-1,-5,-3,-4] => ? = 0
[2,1,5,+,3] => [2,1,5,4,3] => [2,1,5,4,3] => [-2,-1,-5,-4,-3] => ? = 1
[2,1,5,-,3] => [2,1,5,4,3] => [2,1,5,4,3] => [-2,-1,-5,-4,-3] => ? = 1
[2,3,1,5,4] => [2,3,1,5,4] => [2,3,1,5,4] => [-2,-3,-1,-5,-4] => ? = 0
[2,3,5,1,4] => [2,3,5,1,4] => [2,3,5,1,4] => [-2,-3,-5,-1,-4] => ? = 0
[2,3,5,+,1] => [2,3,5,4,1] => [2,3,5,4,1] => [-2,-3,-5,-4,-1] => ? = 0
[2,3,5,-,1] => [2,3,5,4,1] => [2,3,5,4,1] => [-2,-3,-5,-4,-1] => ? = 0
[2,4,1,3,+] => [2,4,1,3,5] => [2,4,1,3,5] => [-2,-4,-1,-3,-5] => ? = 0
[2,4,1,3,-] => [2,4,1,3,5] => [2,4,1,3,5] => [-2,-4,-1,-3,-5] => ? = 0
[2,4,1,5,3] => [2,4,1,5,3] => [2,4,1,5,3] => [-2,-4,-1,-5,-3] => ? = 0
[2,4,+,1,+] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,-,1,+] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,+,1,-] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,-,1,-] => [2,4,3,1,5] => [2,4,3,1,5] => [-2,-4,-3,-1,-5] => ? = 0
[2,4,+,5,1] => [2,4,3,5,1] => [2,4,3,5,1] => [-2,-4,-3,-5,-1] => ? = 0
[2,4,-,5,1] => [2,4,3,5,1] => [2,4,3,5,1] => [-2,-4,-3,-5,-1] => ? = 0
[2,4,5,1,3] => [2,4,5,1,3] => [2,4,5,1,3] => [-2,-4,-5,-1,-3] => ? = 0
[2,4,5,3,1] => [2,4,5,3,1] => [2,4,5,3,1] => [-2,-4,-5,-3,-1] => ? = 0
[2,5,1,3,4] => [2,5,1,3,4] => [2,5,1,3,4] => [-2,-5,-1,-3,-4] => ? = 0
[2,5,1,+,3] => [2,5,1,4,3] => [2,5,1,4,3] => [-2,-5,-1,-4,-3] => ? = 1
[2,5,1,-,3] => [2,5,1,4,3] => [2,5,1,4,3] => [-2,-5,-1,-4,-3] => ? = 1
[2,5,+,1,4] => [2,5,3,1,4] => [2,5,3,1,4] => [-2,-5,-3,-1,-4] => ? = 0
[2,5,-,1,4] => [2,5,3,1,4] => [2,5,3,1,4] => [-2,-5,-3,-1,-4] => ? = 0
[2,5,+,+,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,-,+,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,+,-,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,-,-,1] => [2,5,3,4,1] => [2,5,3,4,1] => [-2,-5,-3,-4,-1] => ? = 0
[2,5,4,1,3] => [2,5,4,1,3] => [2,5,4,1,3] => [-2,-5,-4,-1,-3] => ? = 1
[2,5,4,3,1] => [2,5,4,3,1] => [2,5,4,3,1] => [-2,-5,-4,-3,-1] => ? = 0
[3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => [-3,-1,-2,-5,-4] => ? = 0
[3,1,4,2,+] => [3,1,4,2,5] => [3,1,4,2,5] => [-3,-1,-4,-2,-5] => ? = 0
[3,1,4,2,-] => [3,1,4,2,5] => [3,1,4,2,5] => [-3,-1,-4,-2,-5] => ? = 0
[3,1,4,5,2] => [3,1,4,5,2] => [3,1,4,5,2] => [-3,-1,-4,-5,-2] => ? = 0
[3,1,5,2,4] => [3,1,5,2,4] => [3,1,5,2,4] => [-3,-1,-5,-2,-4] => ? = 0
[3,1,5,+,2] => [3,1,5,4,2] => [3,1,5,4,2] => [-3,-1,-5,-4,-2] => ? = 1
[3,1,5,-,2] => [3,1,5,4,2] => [3,1,5,4,2] => [-3,-1,-5,-4,-2] => ? = 1
[3,+,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,-,1,+,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,+,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,+,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,-,1,-,+] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,-,1,+,-] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
[3,+,1,-,-] => [3,2,1,4,5] => [3,2,1,4,5] => [-3,-2,-1,-4,-5] => ? = 0
Description
The number of alignments of type EN of a signed permutation. An alignment of type EN of a signed permutation π∈Hn is a pair −n≤i≤j≤n, i,j≠0, such that one of the following conditions hold: * $-i < 0 < -\pi(i) < \pi(j) < j$ * $i \leq\pi(i) < \pi(j) < j$.
The following 30 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001868The number of alignments of type NE of a signed permutation. St001889The size of the connectivity set of a signed permutation. St001866The nesting alignments of a signed permutation. St001893The flag descent of a signed permutation. St001845The number of join irreducibles minus the rank of a lattice. St001862The number of crossings of a signed permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001896The number of right descents of a signed permutations. St001892The flag excedance statistic of a signed permutation. St001301The first Betti number of the order complex associated with the poset. St000908The length of the shortest maximal antichain in a poset. St000914The sum of the values of the Möbius function of a poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St000188The area of the Dyck path corresponding to a parking function and the total displacement of a parking function. St000195The number of secondary dinversion pairs of the dyck path corresponding to a parking function. St000943The number of spots the most unlucky car had to go further in a parking function. St001946The number of descents in a parking function. St001371The length of the longest Yamanouchi prefix of a binary word. St001730The number of times the path corresponding to a binary word crosses the base line. St001851The number of Hecke atoms of a signed permutation. St001927Sparre Andersen's number of positives of a signed permutation. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$. St001768The number of reduced words of a signed permutation. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000298The order dimension or Dushnik-Miller dimension of a poset. St000640The rank of the largest boolean interval in a poset. St000907The number of maximal antichains of minimal length in a poset. St001490The number of connected components of a skew partition.