Your data matches 5 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000621
Mp00253: Decorated permutations permutationPermutations
Mp00060: Permutations Robinson-Schensted tableau shapeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St000621: 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]
=> 1
[2,4,1,3] => [2,4,1,3] => [2,2]
=> [2]
=> 1
[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]
=> 1
[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]
=> 1
[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]
=> 1
[-,3,2,5,4] => [1,3,2,5,4] => [3,2]
=> [2]
=> 1
[+,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> 1
[-,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> 1
[+,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]
=> 1
[-,4,2,5,3] => [1,4,2,5,3] => [3,2]
=> [2]
=> 1
[+,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 standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is even. This notion was used in [1, Proposition 2.3], see also [2, Theorem 1.1]. The case of an odd minimum is [[St000620]].
Matching statistic: St001092
Mp00253: Decorated permutations permutationPermutations
Mp00060: Permutations Robinson-Schensted tableau shapeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001092: 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]
=> 1
[2,4,1,3] => [2,4,1,3] => [2,2]
=> [2]
=> 1
[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]
=> 1
[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]
=> 1
[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]
=> 1
[-,3,2,5,4] => [1,3,2,5,4] => [3,2]
=> [2]
=> 1
[+,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> 1
[-,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> 1
[+,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]
=> 1
[-,4,2,5,3] => [1,4,2,5,3] => [3,2]
=> [2]
=> 1
[+,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 distinct even parts of a partition. See Section 3.3.1 of [1].
Matching statistic: St001587
Mp00253: Decorated permutations permutationPermutations
Mp00060: Permutations Robinson-Schensted tableau shapeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St001587: 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]
=> 1
[2,4,1,3] => [2,4,1,3] => [2,2]
=> [2]
=> 1
[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]
=> 1
[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]
=> 1
[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]
=> 1
[-,3,2,5,4] => [1,3,2,5,4] => [3,2]
=> [2]
=> 1
[+,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> 1
[-,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> 1
[+,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]
=> 1
[-,4,2,5,3] => [1,4,2,5,3] => [3,2]
=> [2]
=> 1
[+,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
Half of the largest even part of an integer partition. The largest even part is recorded by [[St000995]].
Matching statistic: St000755
Mp00253: Decorated permutations permutationPermutations
Mp00060: Permutations Robinson-Schensted tableau shapeInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
St000755: 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]
=> 1 = 0 + 1
[3,-,1] => [3,2,1] => [1,1,1]
=> [1,1]
=> 1 = 0 + 1
[+,4,+,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[-,4,+,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[+,4,-,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[-,4,-,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 2 = 1 + 1
[2,4,1,3] => [2,4,1,3] => [2,2]
=> [2]
=> 2 = 1 + 1
[2,4,+,1] => [2,4,3,1] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[2,4,-,1] => [2,4,3,1] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[3,1,4,2] => [3,1,4,2] => [2,2]
=> [2]
=> 2 = 1 + 1
[3,+,1,+] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[3,-,1,+] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[3,+,1,-] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[3,-,1,-] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[3,+,4,1] => [3,2,4,1] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[3,-,4,1] => [3,2,4,1] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[3,4,1,2] => [3,4,1,2] => [2,2]
=> [2]
=> 2 = 1 + 1
[3,4,2,1] => [3,4,2,1] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[4,1,+,2] => [4,1,3,2] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[4,1,-,2] => [4,1,3,2] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[4,+,1,3] => [4,2,1,3] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[4,-,1,3] => [4,2,1,3] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[4,+,+,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[4,-,+,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[4,+,-,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[4,-,-,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[4,3,1,2] => [4,3,1,2] => [2,1,1]
=> [1,1]
=> 1 = 0 + 1
[4,3,2,1] => [4,3,2,1] => [1,1,1,1]
=> [1,1,1]
=> 1 = 0 + 1
[+,+,5,+,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[-,+,5,+,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[+,-,5,+,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[+,+,5,-,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[-,-,5,+,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[-,+,5,-,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[+,-,5,-,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[-,-,5,-,3] => [1,2,5,4,3] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[+,3,2,5,4] => [1,3,2,5,4] => [3,2]
=> [2]
=> 2 = 1 + 1
[-,3,2,5,4] => [1,3,2,5,4] => [3,2]
=> [2]
=> 2 = 1 + 1
[+,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> 2 = 1 + 1
[-,3,5,2,4] => [1,3,5,2,4] => [3,2]
=> [2]
=> 2 = 1 + 1
[+,3,5,+,2] => [1,3,5,4,2] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[-,3,5,+,2] => [1,3,5,4,2] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[+,3,5,-,2] => [1,3,5,4,2] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[-,3,5,-,2] => [1,3,5,4,2] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[+,4,2,5,3] => [1,4,2,5,3] => [3,2]
=> [2]
=> 2 = 1 + 1
[-,4,2,5,3] => [1,4,2,5,3] => [3,2]
=> [2]
=> 2 = 1 + 1
[+,4,+,2,+] => [1,4,3,2,5] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[-,4,+,2,+] => [1,4,3,2,5] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
[+,4,-,2,+] => [1,4,3,2,5] => [3,1,1]
=> [1,1]
=> 1 = 0 + 1
Description
The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. Consider the recurrence $$f(n)=\sum_{p\in\lambda} f(n-p).$$ This statistic returns the number of distinct real roots of the associated characteristic polynomial. For example, the partition $(2,1)$ corresponds to the recurrence $f(n)=f(n-1)+f(n-2)$ with associated characteristic polynomial $x^2-x-1$, which has two real roots.
Mp00253: Decorated permutations permutationPermutations
Mp00069: Permutations complementPermutations
Mp00170: Permutations to signed permutationSigned permutations
St001768: Signed permutations ⟶ ℤResult quality: 1% values known / values provided: 1%distinct values known / distinct values provided: 100%
Values
[3,+,1] => [3,2,1] => [1,2,3] => [1,2,3] => 1 = 0 + 1
[3,-,1] => [3,2,1] => [1,2,3] => [1,2,3] => 1 = 0 + 1
[+,4,+,2] => [1,4,3,2] => [4,1,2,3] => [4,1,2,3] => 1 = 0 + 1
[-,4,+,2] => [1,4,3,2] => [4,1,2,3] => [4,1,2,3] => 1 = 0 + 1
[+,4,-,2] => [1,4,3,2] => [4,1,2,3] => [4,1,2,3] => 1 = 0 + 1
[-,4,-,2] => [1,4,3,2] => [4,1,2,3] => [4,1,2,3] => 1 = 0 + 1
[2,1,4,3] => [2,1,4,3] => [3,4,1,2] => [3,4,1,2] => 2 = 1 + 1
[2,4,1,3] => [2,4,1,3] => [3,1,4,2] => [3,1,4,2] => 2 = 1 + 1
[2,4,+,1] => [2,4,3,1] => [3,1,2,4] => [3,1,2,4] => 1 = 0 + 1
[2,4,-,1] => [2,4,3,1] => [3,1,2,4] => [3,1,2,4] => 1 = 0 + 1
[3,1,4,2] => [3,1,4,2] => [2,4,1,3] => [2,4,1,3] => 2 = 1 + 1
[3,+,1,+] => [3,2,1,4] => [2,3,4,1] => [2,3,4,1] => 1 = 0 + 1
[3,-,1,+] => [3,2,1,4] => [2,3,4,1] => [2,3,4,1] => 1 = 0 + 1
[3,+,1,-] => [3,2,1,4] => [2,3,4,1] => [2,3,4,1] => 1 = 0 + 1
[3,-,1,-] => [3,2,1,4] => [2,3,4,1] => [2,3,4,1] => 1 = 0 + 1
[3,+,4,1] => [3,2,4,1] => [2,3,1,4] => [2,3,1,4] => 1 = 0 + 1
[3,-,4,1] => [3,2,4,1] => [2,3,1,4] => [2,3,1,4] => 1 = 0 + 1
[3,4,1,2] => [3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 2 = 1 + 1
[3,4,2,1] => [3,4,2,1] => [2,1,3,4] => [2,1,3,4] => 1 = 0 + 1
[4,1,+,2] => [4,1,3,2] => [1,4,2,3] => [1,4,2,3] => 1 = 0 + 1
[4,1,-,2] => [4,1,3,2] => [1,4,2,3] => [1,4,2,3] => 1 = 0 + 1
[4,+,1,3] => [4,2,1,3] => [1,3,4,2] => [1,3,4,2] => 1 = 0 + 1
[4,-,1,3] => [4,2,1,3] => [1,3,4,2] => [1,3,4,2] => 1 = 0 + 1
[4,+,+,1] => [4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 1 = 0 + 1
[4,-,+,1] => [4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 1 = 0 + 1
[4,+,-,1] => [4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 1 = 0 + 1
[4,-,-,1] => [4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 1 = 0 + 1
[4,3,1,2] => [4,3,1,2] => [1,2,4,3] => [1,2,4,3] => 1 = 0 + 1
[4,3,2,1] => [4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 1 = 0 + 1
[+,+,5,+,3] => [1,2,5,4,3] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 0 + 1
[-,+,5,+,3] => [1,2,5,4,3] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 0 + 1
[+,-,5,+,3] => [1,2,5,4,3] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 0 + 1
[+,+,5,-,3] => [1,2,5,4,3] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 0 + 1
[-,-,5,+,3] => [1,2,5,4,3] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 0 + 1
[-,+,5,-,3] => [1,2,5,4,3] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 0 + 1
[+,-,5,-,3] => [1,2,5,4,3] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 0 + 1
[-,-,5,-,3] => [1,2,5,4,3] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 0 + 1
[+,3,2,5,4] => [1,3,2,5,4] => [5,3,4,1,2] => [5,3,4,1,2] => ? = 1 + 1
[-,3,2,5,4] => [1,3,2,5,4] => [5,3,4,1,2] => [5,3,4,1,2] => ? = 1 + 1
[+,3,5,2,4] => [1,3,5,2,4] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 1 + 1
[-,3,5,2,4] => [1,3,5,2,4] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 1 + 1
[+,3,5,+,2] => [1,3,5,4,2] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 0 + 1
[-,3,5,+,2] => [1,3,5,4,2] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 0 + 1
[+,3,5,-,2] => [1,3,5,4,2] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 0 + 1
[-,3,5,-,2] => [1,3,5,4,2] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 0 + 1
[+,4,2,5,3] => [1,4,2,5,3] => [5,2,4,1,3] => [5,2,4,1,3] => ? = 1 + 1
[-,4,2,5,3] => [1,4,2,5,3] => [5,2,4,1,3] => [5,2,4,1,3] => ? = 1 + 1
[+,4,+,2,+] => [1,4,3,2,5] => [5,2,3,4,1] => [5,2,3,4,1] => ? = 0 + 1
[-,4,+,2,+] => [1,4,3,2,5] => [5,2,3,4,1] => [5,2,3,4,1] => ? = 0 + 1
[+,4,-,2,+] => [1,4,3,2,5] => [5,2,3,4,1] => [5,2,3,4,1] => ? = 0 + 1
[+,4,+,2,-] => [1,4,3,2,5] => [5,2,3,4,1] => [5,2,3,4,1] => ? = 0 + 1
[-,4,-,2,+] => [1,4,3,2,5] => [5,2,3,4,1] => [5,2,3,4,1] => ? = 0 + 1
[-,4,+,2,-] => [1,4,3,2,5] => [5,2,3,4,1] => [5,2,3,4,1] => ? = 0 + 1
[+,4,-,2,-] => [1,4,3,2,5] => [5,2,3,4,1] => [5,2,3,4,1] => ? = 0 + 1
[-,4,-,2,-] => [1,4,3,2,5] => [5,2,3,4,1] => [5,2,3,4,1] => ? = 0 + 1
[+,4,+,5,2] => [1,4,3,5,2] => [5,2,3,1,4] => [5,2,3,1,4] => ? = 0 + 1
[-,4,+,5,2] => [1,4,3,5,2] => [5,2,3,1,4] => [5,2,3,1,4] => ? = 0 + 1
[+,4,-,5,2] => [1,4,3,5,2] => [5,2,3,1,4] => [5,2,3,1,4] => ? = 0 + 1
[-,4,-,5,2] => [1,4,3,5,2] => [5,2,3,1,4] => [5,2,3,1,4] => ? = 0 + 1
[+,4,5,2,3] => [1,4,5,2,3] => [5,2,1,4,3] => [5,2,1,4,3] => ? = 1 + 1
[-,4,5,2,3] => [1,4,5,2,3] => [5,2,1,4,3] => [5,2,1,4,3] => ? = 1 + 1
[+,4,5,3,2] => [1,4,5,3,2] => [5,2,1,3,4] => [5,2,1,3,4] => ? = 0 + 1
[-,4,5,3,2] => [1,4,5,3,2] => [5,2,1,3,4] => [5,2,1,3,4] => ? = 0 + 1
[+,5,2,+,3] => [1,5,2,4,3] => [5,1,4,2,3] => [5,1,4,2,3] => ? = 0 + 1
[-,5,2,+,3] => [1,5,2,4,3] => [5,1,4,2,3] => [5,1,4,2,3] => ? = 0 + 1
[+,5,2,-,3] => [1,5,2,4,3] => [5,1,4,2,3] => [5,1,4,2,3] => ? = 0 + 1
[-,5,2,-,3] => [1,5,2,4,3] => [5,1,4,2,3] => [5,1,4,2,3] => ? = 0 + 1
[+,5,+,2,4] => [1,5,3,2,4] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 0 + 1
[-,5,+,2,4] => [1,5,3,2,4] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 0 + 1
[+,5,-,2,4] => [1,5,3,2,4] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 0 + 1
[-,5,-,2,4] => [1,5,3,2,4] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 0 + 1
[+,5,+,+,2] => [1,5,3,4,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 0 + 1
[-,5,+,+,2] => [1,5,3,4,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 0 + 1
[+,5,-,+,2] => [1,5,3,4,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 0 + 1
[+,5,+,-,2] => [1,5,3,4,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 0 + 1
[-,5,-,+,2] => [1,5,3,4,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 0 + 1
[-,5,+,-,2] => [1,5,3,4,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 0 + 1
[+,5,-,-,2] => [1,5,3,4,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 0 + 1
[-,5,-,-,2] => [1,5,3,4,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 0 + 1
Description
The number of reduced words of a signed permutation. This is the number of ways to write a permutation as a minimal length product of simple reflections.