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Matching statistic: St001714
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001714: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001714: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,1]
=> [1]
=> 0
[1,-2] => [1,2] => [1,1]
=> [1]
=> 0
[-1,2] => [1,2] => [1,1]
=> [1]
=> 0
[-1,-2] => [1,2] => [1,1]
=> [1]
=> 0
[1,2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[1,2,-3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[1,-2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[1,-2,-3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[-1,2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[-1,2,-3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[-1,-2,3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[-1,-2,-3] => [1,2,3] => [1,1,1]
=> [1,1]
=> 1
[1,3,2] => [1,3,2] => [2,1]
=> [1]
=> 0
[1,3,-2] => [1,3,2] => [2,1]
=> [1]
=> 0
[1,-3,2] => [1,3,2] => [2,1]
=> [1]
=> 0
[1,-3,-2] => [1,3,2] => [2,1]
=> [1]
=> 0
[-1,3,2] => [1,3,2] => [2,1]
=> [1]
=> 0
[-1,3,-2] => [1,3,2] => [2,1]
=> [1]
=> 0
[-1,-3,2] => [1,3,2] => [2,1]
=> [1]
=> 0
[-1,-3,-2] => [1,3,2] => [2,1]
=> [1]
=> 0
[2,1,3] => [2,1,3] => [2,1]
=> [1]
=> 0
[2,1,-3] => [2,1,3] => [2,1]
=> [1]
=> 0
[2,-1,3] => [2,1,3] => [2,1]
=> [1]
=> 0
[2,-1,-3] => [2,1,3] => [2,1]
=> [1]
=> 0
[-2,1,3] => [2,1,3] => [2,1]
=> [1]
=> 0
[-2,1,-3] => [2,1,3] => [2,1]
=> [1]
=> 0
[-2,-1,3] => [2,1,3] => [2,1]
=> [1]
=> 0
[-2,-1,-3] => [2,1,3] => [2,1]
=> [1]
=> 0
[3,2,1] => [3,2,1] => [2,1]
=> [1]
=> 0
[3,2,-1] => [3,2,1] => [2,1]
=> [1]
=> 0
[3,-2,1] => [3,2,1] => [2,1]
=> [1]
=> 0
[3,-2,-1] => [3,2,1] => [2,1]
=> [1]
=> 0
[-3,2,1] => [3,2,1] => [2,1]
=> [1]
=> 0
[-3,2,-1] => [3,2,1] => [2,1]
=> [1]
=> 0
[-3,-2,1] => [3,2,1] => [2,1]
=> [1]
=> 0
[-3,-2,-1] => [3,2,1] => [2,1]
=> [1]
=> 0
[1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,2,3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,2,-3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,2,-3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,-2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,-2,3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,-2,-3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[1,-2,-3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[-1,2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[-1,2,3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[-1,2,-3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[-1,2,-3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[-1,-2,3,4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
[-1,-2,3,-4] => [1,2,3,4] => [1,1,1,1]
=> [1,1,1]
=> 2
Description
The number of subpartitions of an integer partition that do not dominate the conjugate subpartition.
In particular, partitions with statistic $0$ are wide partitions.
Matching statistic: St000942
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St000942: Parking functions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 60%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St000942: Parking functions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 60%
Values
[1,2] => [1,2] => [1,2] => [1,2] => 2 = 0 + 2
[1,-2] => [1,2] => [1,2] => [1,2] => 2 = 0 + 2
[-1,2] => [1,2] => [1,2] => [1,2] => 2 = 0 + 2
[-1,-2] => [1,2] => [1,2] => [1,2] => 2 = 0 + 2
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 1 + 2
[1,2,-3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 1 + 2
[1,-2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 1 + 2
[1,-2,-3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 1 + 2
[-1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 1 + 2
[-1,2,-3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 1 + 2
[-1,-2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 1 + 2
[-1,-2,-3] => [1,2,3] => [1,2,3] => [1,2,3] => 3 = 1 + 2
[1,3,2] => [1,3,2] => [1,3,2] => [1,3,2] => 2 = 0 + 2
[1,3,-2] => [1,3,2] => [1,3,2] => [1,3,2] => 2 = 0 + 2
[1,-3,2] => [1,3,2] => [1,3,2] => [1,3,2] => 2 = 0 + 2
[1,-3,-2] => [1,3,2] => [1,3,2] => [1,3,2] => 2 = 0 + 2
[-1,3,2] => [1,3,2] => [1,3,2] => [1,3,2] => 2 = 0 + 2
[-1,3,-2] => [1,3,2] => [1,3,2] => [1,3,2] => 2 = 0 + 2
[-1,-3,2] => [1,3,2] => [1,3,2] => [1,3,2] => 2 = 0 + 2
[-1,-3,-2] => [1,3,2] => [1,3,2] => [1,3,2] => 2 = 0 + 2
[2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 2 = 0 + 2
[2,1,-3] => [2,1,3] => [2,1,3] => [2,1,3] => 2 = 0 + 2
[2,-1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 2 = 0 + 2
[2,-1,-3] => [2,1,3] => [2,1,3] => [2,1,3] => 2 = 0 + 2
[-2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 2 = 0 + 2
[-2,1,-3] => [2,1,3] => [2,1,3] => [2,1,3] => 2 = 0 + 2
[-2,-1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 2 = 0 + 2
[-2,-1,-3] => [2,1,3] => [2,1,3] => [2,1,3] => 2 = 0 + 2
[3,2,1] => [3,2,1] => [2,3,1] => [2,3,1] => 2 = 0 + 2
[3,2,-1] => [3,2,1] => [2,3,1] => [2,3,1] => 2 = 0 + 2
[3,-2,1] => [3,2,1] => [2,3,1] => [2,3,1] => 2 = 0 + 2
[3,-2,-1] => [3,2,1] => [2,3,1] => [2,3,1] => 2 = 0 + 2
[-3,2,1] => [3,2,1] => [2,3,1] => [2,3,1] => 2 = 0 + 2
[-3,2,-1] => [3,2,1] => [2,3,1] => [2,3,1] => 2 = 0 + 2
[-3,-2,1] => [3,2,1] => [2,3,1] => [2,3,1] => 2 = 0 + 2
[-3,-2,-1] => [3,2,1] => [2,3,1] => [2,3,1] => 2 = 0 + 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[-1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[-1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[-1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[-1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[-1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[-1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4 = 2 + 2
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,2,3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,2,3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,2,3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,2,-3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,2,-3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,2,-3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,2,-3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,-2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,-2,3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,-2,3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,-2,3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,-2,-3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,-2,-3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,-2,-3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,-2,-3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,2,3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,2,3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,2,3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,2,-3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,2,-3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,2,-3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,2,-3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,-2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,-2,3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,-2,3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,-2,3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,-2,-3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,-2,-3,4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,-2,-3,-4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[-1,-2,-3,-4,-5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 3 + 2
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,2,3,5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,2,3,-5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,2,3,-5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,2,-3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,2,-3,5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,2,-3,-5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,2,-3,-5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,-2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,-2,3,5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,-2,3,-5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,-2,3,-5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,-2,-3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,-2,-3,5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,-2,-3,-5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[1,-2,-3,-5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[-1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
[-1,2,3,5,-4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 + 2
Description
The number of critical left to right maxima of the parking functions.
An entry $p$ in a parking function is critical, if there are exactly $p-1$ entries smaller than $p$ and $n-p$ entries larger than $p$. It is a left to right maximum, if there are no larger entries before it.
This statistic allows the computation of the Tutte polynomial of the complete graph $K_{n+1}$, via
$$
\sum_{P} x^{st(P)}y^{\binom{n+1}{2}-\sum P},
$$
where the sum is over all parking functions of length $n$, see [1, thm.13.5.16].
Matching statistic: St001857
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 40%
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 40%
Values
[1,2] => [1,2] => [2,1] => [2,1] => 0
[1,-2] => [1,2] => [2,1] => [2,1] => 0
[-1,2] => [1,2] => [2,1] => [2,1] => 0
[-1,-2] => [1,2] => [2,1] => [2,1] => 0
[1,2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,-2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,-2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[-1,2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[-1,2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[-1,-2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[-1,-2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[1,3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[1,-3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[1,-3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[-1,3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[-1,3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[-1,-3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[-1,-3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[2,1,3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[2,1,-3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[2,-1,3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[2,-1,-3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[-2,1,3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[-2,1,-3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[-2,-1,3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[-2,-1,-3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[3,2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[3,2,-1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[3,-2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[3,-2,-1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[-3,2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[-3,2,-1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[-3,-2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[-3,-2,-1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[1,2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[1,2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[1,2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[1,-2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[1,-2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[1,-2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[1,-2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[-1,2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[-1,2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[-1,2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[-1,2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[-1,-2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[-1,-2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[-1,-2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[-1,-2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 2
[1,2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,-2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,-2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,-2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,-2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,-2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,-2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,-2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,-2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,-3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,-3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,-3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,-3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,-3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,-3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,-3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,-3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,3,4,2] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => ? = 0
[1,3,4,-2] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => ? = 0
Description
The number of edges in the reduced word graph of a signed permutation.
The reduced word graph of a signed permutation $\pi$ has the reduced words of $\pi$ as vertices and an edge between two reduced words if they differ by exactly one braid move.
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