Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001714
Mapping
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ 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] => [1,0,1,0]
 => [1]
 => 0
[1,-2] => [1,2] => [1,0,1,0]
 => [1]
 => 0
[-1,2] => [1,2] => [1,0,1,0]
 => [1]
 => 0
[-1,-2] => [1,2] => [1,0,1,0]
 => [1]
 => 0
[1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => [2,1]
 => 0
[1,2,-3] => [1,2,3] => [1,0,1,0,1,0]
 => [2,1]
 => 0
[1,-2,3] => [1,2,3] => [1,0,1,0,1,0]
 => [2,1]
 => 0
[1,-2,-3] => [1,2,3] => [1,0,1,0,1,0]
 => [2,1]
 => 0
[-1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => [2,1]
 => 0
[-1,2,-3] => [1,2,3] => [1,0,1,0,1,0]
 => [2,1]
 => 0
[-1,-2,3] => [1,2,3] => [1,0,1,0,1,0]
 => [2,1]
 => 0
[-1,-2,-3] => [1,2,3] => [1,0,1,0,1,0]
 => [2,1]
 => 0
[1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1]
 => 1
[1,3,-2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1]
 => 1
[1,-3,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1]
 => 1
[1,-3,-2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1]
 => 1
[-1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1]
 => 1
[-1,3,-2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1]
 => 1
[-1,-3,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1]
 => 1
[-1,-3,-2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1]
 => 1
[2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => [2]
 => 0
[2,1,-3] => [2,1,3] => [1,1,0,0,1,0]
 => [2]
 => 0
[2,-1,3] => [2,1,3] => [1,1,0,0,1,0]
 => [2]
 => 0
[2,-1,-3] => [2,1,3] => [1,1,0,0,1,0]
 => [2]
 => 0
[-2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => [2]
 => 0
[-2,1,-3] => [2,1,3] => [1,1,0,0,1,0]
 => [2]
 => 0
[-2,-1,3] => [2,1,3] => [1,1,0,0,1,0]
 => [2]
 => 0
[-2,-1,-3] => [2,1,3] => [1,1,0,0,1,0]
 => [2]
 => 0
[2,3,1] => [2,3,1] => [1,1,0,1,0,0]
 => [1]
 => 0
[2,3,-1] => [2,3,1] => [1,1,0,1,0,0]
 => [1]
 => 0
[2,-3,1] => [2,3,1] => [1,1,0,1,0,0]
 => [1]
 => 0
[2,-3,-1] => [2,3,1] => [1,1,0,1,0,0]
 => [1]
 => 0
[-2,3,1] => [2,3,1] => [1,1,0,1,0,0]
 => [1]
 => 0
[-2,3,-1] => [2,3,1] => [1,1,0,1,0,0]
 => [1]
 => 0
[-2,-3,1] => [2,3,1] => [1,1,0,1,0,0]
 => [1]
 => 0
[-2,-3,-1] => [2,3,1] => [1,1,0,1,0,0]
 => [1]
 => 0
[1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[1,2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[1,2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[1,2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[1,-2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[1,-2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[1,-2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[1,-2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[-1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[-1,2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[-1,2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[-1,2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[-1,-2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
[-1,-2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 0
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: St001330
Mapping
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 7%
Values
[1,2] => [1,2] => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
[1,-2] => [1,2] => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
[-1,2] => [1,2] => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
[-1,-2] => [1,2] => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
[1,2,3] => [1,2,3] => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
[1,2,-3] => [1,2,3] => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
[1,-2,3] => [1,2,3] => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
[1,-2,-3] => [1,2,3] => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
[-1,2,3] => [1,2,3] => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
[-1,2,-3] => [1,2,3] => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
[-1,-2,3] => [1,2,3] => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
[-1,-2,-3] => [1,2,3] => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
[1,3,2] => [1,3,2] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 2
[1,3,-2] => [1,3,2] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 2
[1,-3,2] => [1,3,2] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 2
[1,-3,-2] => [1,3,2] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 2
[-1,3,2] => [1,3,2] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 2
[-1,3,-2] => [1,3,2] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 2
[-1,-3,2] => [1,3,2] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 2
[-1,-3,-2] => [1,3,2] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 2
[2,1,3] => [2,1,3] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[2,1,-3] => [2,1,3] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[2,-1,3] => [2,1,3] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[2,-1,-3] => [2,1,3] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[-2,1,3] => [2,1,3] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[-2,1,-3] => [2,1,3] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[-2,-1,3] => [2,1,3] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[-2,-1,-3] => [2,1,3] => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[2,3,1] => [2,3,1] => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[2,3,-1] => [2,3,1] => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[2,-3,1] => [2,3,1] => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[2,-3,-1] => [2,3,1] => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[-2,3,1] => [2,3,1] => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[-2,3,-1] => [2,3,1] => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[-2,-3,1] => [2,3,1] => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[-2,-3,-1] => [2,3,1] => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[1,2,3,4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,2,3,-4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,2,-3,4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,2,-3,-4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,-2,3,4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,-2,3,-4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,-2,-3,4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,-2,-3,-4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[-1,2,3,4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[-1,2,3,-4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[-1,2,-3,4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[-1,2,-3,-4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[-1,-2,3,4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[-1,-2,3,-4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[-1,-2,-3,4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[-1,-2,-3,-4] => [1,2,3,4] => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,2,4,-3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,2,-4,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,2,-4,-3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,-2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,-2,4,-3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,-2,-4,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,-2,-4,-3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[-1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[-1,2,4,-3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[-1,2,-4,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[-1,2,-4,-3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[-1,-2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[-1,-2,4,-3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[-1,-2,-4,3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[-1,-2,-4,-3] => [1,2,4,3] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,3,2,-4] => [1,3,2,4] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,3,-2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,3,-2,-4] => [1,3,2,4] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,-3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,-3,2,-4] => [1,3,2,4] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,-3,-2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,-3,-2,-4] => [1,3,2,4] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[-1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[-1,3,2,-4] => [1,3,2,4] => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,2,3,4,-5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,2,3,-4,5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,2,3,-4,-5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,2,-3,4,5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,2,-3,4,-5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,2,-3,-4,5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,2,-3,-4,-5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,-2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,-2,3,4,-5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,-2,3,-4,5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,-2,3,-4,-5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,-2,-3,4,5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,-2,-3,4,-5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,-2,-3,-4,5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,-2,-3,-4,-5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-1,2,3,4,-5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-1,2,3,-4,5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-1,2,3,-4,-5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-1,2,-3,4,5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-1,2,-3,4,-5] => [1,2,3,4,5] => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
Description
The hat guessing number of a graph. Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors. Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Matching statistic: St001857
Mapping
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras 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: 14%
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] => [2,3,1] => [2,3,1] => 0
[1,2,-3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,-2,3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,-2,-3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[-1,2,3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[-1,2,-3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[-1,-2,3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[-1,-2,-3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,3,2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[1,3,-2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[1,-3,2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[1,-3,-2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[-1,3,2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[-1,3,-2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[-1,-3,2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[-1,-3,-2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[2,1,3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[2,1,-3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[2,-1,3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[2,-1,-3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[-2,1,3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[-2,1,-3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[-2,-1,3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[-2,-1,-3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[2,3,1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[2,3,-1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[2,-3,1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[2,-3,-1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[-2,3,1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[-2,3,-1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[-2,-3,1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[-2,-3,-1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,2,3,-4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,2,-3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,2,-3,-4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,-2,3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,-2,3,-4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,-2,-3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,-2,-3,-4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[-1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[-1,2,3,-4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[-1,2,-3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[-1,2,-3,-4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[-1,-2,3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[-1,-2,3,-4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[-1,-2,-3,4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[-1,-2,-3,-4] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => ? = 0
[1,2,4,3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[1,2,4,-3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[1,2,-4,3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[1,2,-4,-3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[1,-2,4,3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[1,-2,4,-3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[1,-2,-4,3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[1,-2,-4,-3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[-1,2,4,3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[-1,2,4,-3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[-1,2,-4,3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[-1,2,-4,-3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[-1,-2,4,3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[-1,-2,4,-3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[-1,-2,-4,3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[-1,-2,-4,-3] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => ? = 1
[1,3,2,4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[1,3,2,-4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[1,3,-2,4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[1,3,-2,-4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[1,-3,2,4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[1,-3,2,-4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[1,-3,-2,4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[1,-3,-2,-4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[-1,3,2,4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[-1,3,2,-4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[-1,3,-2,4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[-1,3,-2,-4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[-1,-3,2,4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[-1,-3,2,-4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[-1,-3,-2,4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[-1,-3,-2,-4] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => ? = 1
[1,3,4,2] => [1,3,4,2] => [4,2,3,1] => [4,2,3,1] => ? = 2
[1,3,4,-2] => [1,3,4,2] => [4,2,3,1] => [4,2,3,1] => ? = 2
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.