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Your data matches 6 different statistics following compositions of up to 3 maps.
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Matching statistic: St000934
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000934: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000934: 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 2-degree of an integer partition.
For an integer partition $\lambda$, this is given by the exponent of 2 in the Gram determinant of the integal Specht module of the symmetric group indexed by $\lambda$.
Matching statistic: St000260
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 33%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 33%
Values
[3,+,1] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,-,1] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? = 0 + 1
[+,4,+,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[-,4,+,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[+,4,-,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[-,4,-,2] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 1
[2,1,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 1
[2,4,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 1
[2,4,+,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[2,4,-,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 1
[3,1,4,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 1
[3,+,1,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[3,-,1,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[3,+,1,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[3,-,1,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 0 + 1
[3,+,4,1] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[3,-,4,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 1
[3,4,1,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 1
[3,4,2,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[4,1,+,2] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,1,-,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[4,+,1,3] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,-,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[4,+,+,1] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,-,+,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[4,+,-,1] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[4,-,-,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 1
[4,3,1,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[4,3,2,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[+,+,5,+,3] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[-,+,5,+,3] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[+,-,5,+,3] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[+,+,5,-,3] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[-,-,5,+,3] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[-,+,5,-,3] => [2,5,1,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[+,-,5,-,3] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[-,-,5,-,3] => [5,1,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 0 + 1
[+,3,2,5,4] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 1
[-,3,2,5,4] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 1
[+,3,5,2,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 1
[-,3,5,2,4] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 1
[+,3,5,+,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[-,3,5,+,2] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[+,3,5,-,2] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[-,3,5,-,2] => [5,1,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 0 + 1
[+,4,2,5,3] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 1
[-,4,2,5,3] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 1
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[-,4,+,2,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[+,4,-,2,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[+,4,+,2,-] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[-,4,-,2,+] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[-,4,+,2,-] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[+,4,-,2,-] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[-,4,-,2,-] => [4,1,2,3,5] => [1,4] => ([(3,4)],5)
=> ? = 0 + 1
[+,4,+,5,2] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[-,4,+,5,2] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[+,4,-,5,2] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[+,5,2,+,3] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[+,5,+,2,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,+,1,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[4,1,+,2,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[4,+,1,3,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[4,+,+,1,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,1,2,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,1,+,2,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,1,+,+,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,+,1,3,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,+,1,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,+,+,1,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,+,+,+,1] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[+,+,+,6,+,4] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,+,5,+,3,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,+,6,3,+,4] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,+,6,+,3,5] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,+,6,+,+,3] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,4,+,2,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,5,2,+,3,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,5,+,2,4,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,5,+,+,2,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,2,3,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,2,+,3,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,2,+,+,3] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,+,2,4,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,+,2,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,+,+,2,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,+,+,+,2] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[3,+,1,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[4,1,+,2,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[4,+,1,3,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[4,+,+,1,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,1,2,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,1,+,2,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,1,+,+,2,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,+,1,3,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,+,1,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,+,+,1,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,+,+,+,1,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[6,1,2,3,+,4] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St000456
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 33%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 33%
Values
[3,+,1] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1 = 0 + 1
[3,-,1] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? = 0 + 1
[+,4,+,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[-,4,+,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[+,4,-,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[-,4,-,2] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 1
[2,1,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 1
[2,4,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 1
[2,4,+,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[2,4,-,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 1
[3,1,4,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 1
[3,+,1,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[3,-,1,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[3,+,1,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[3,-,1,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 0 + 1
[3,+,4,1] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[3,-,4,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 1
[3,4,1,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 1
[3,4,2,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[4,1,+,2] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,1,-,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[4,+,1,3] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,-,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[4,+,+,1] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 0 + 1
[4,-,+,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[4,+,-,1] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[4,-,-,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 1
[4,3,1,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[4,3,2,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
[+,+,5,+,3] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[-,+,5,+,3] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[+,-,5,+,3] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[+,+,5,-,3] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[-,-,5,+,3] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[-,+,5,-,3] => [2,5,1,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[+,-,5,-,3] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[-,-,5,-,3] => [5,1,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 0 + 1
[+,3,2,5,4] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 1
[-,3,2,5,4] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 1
[+,3,5,2,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 1
[-,3,5,2,4] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 1
[+,3,5,+,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[-,3,5,+,2] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[+,3,5,-,2] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[-,3,5,-,2] => [5,1,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 0 + 1
[+,4,2,5,3] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 1
[-,4,2,5,3] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 1
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[-,4,+,2,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[+,4,-,2,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[+,4,+,2,-] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[-,4,-,2,+] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[-,4,+,2,-] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[+,4,-,2,-] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[-,4,-,2,-] => [4,1,2,3,5] => [1,4] => ([(3,4)],5)
=> ? = 0 + 1
[+,4,+,5,2] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 1
[-,4,+,5,2] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[+,4,-,5,2] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 1
[+,5,2,+,3] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[+,5,+,2,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[3,+,1,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[4,1,+,2,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[4,+,1,3,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[4,+,+,1,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,1,2,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,1,+,2,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,1,+,+,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,+,1,3,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,+,1,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,+,+,1,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[5,+,+,+,1] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 0 + 1
[+,+,+,6,+,4] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,+,5,+,3,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,+,6,3,+,4] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,+,6,+,3,5] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,+,6,+,+,3] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,4,+,2,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,5,2,+,3,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,5,+,2,4,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,5,+,+,2,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,2,3,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,2,+,3,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,2,+,+,3] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,+,2,4,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,+,2,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,+,+,2,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[+,6,+,+,+,2] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[3,+,1,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[4,1,+,2,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[4,+,1,3,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[4,+,+,1,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,1,2,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,1,+,2,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,1,+,+,2,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,+,1,3,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,+,1,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,+,+,1,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[5,+,+,+,1,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
[6,1,2,3,+,4] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 0 + 1
Description
The monochromatic index of a connected graph.
This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path.
For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
Matching statistic: St000259
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 33%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 33%
Values
[3,+,1] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 0 + 2
[3,-,1] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? = 0 + 2
[+,4,+,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[-,4,+,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[+,4,-,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[-,4,-,2] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 2
[2,1,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 2
[2,4,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 2
[2,4,+,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[2,4,-,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 2
[3,1,4,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 2
[3,+,1,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[3,-,1,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[3,+,1,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[3,-,1,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 0 + 2
[3,+,4,1] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[3,-,4,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 2
[3,4,1,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 2
[3,4,2,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[4,1,+,2] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[4,1,-,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[4,+,1,3] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[4,-,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[4,+,+,1] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 0 + 2
[4,-,+,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[4,+,-,1] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[4,-,-,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 2
[4,3,1,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[4,3,2,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 2
[+,+,5,+,3] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[-,+,5,+,3] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 2
[+,-,5,+,3] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 2
[+,+,5,-,3] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 2
[-,-,5,+,3] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[-,+,5,-,3] => [2,5,1,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[+,-,5,-,3] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[-,-,5,-,3] => [5,1,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 0 + 2
[+,3,2,5,4] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
[-,3,2,5,4] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 2
[+,3,5,2,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
[-,3,5,2,4] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 2
[+,3,5,+,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 2
[-,3,5,+,2] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[+,3,5,-,2] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[-,3,5,-,2] => [5,1,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 0 + 2
[+,4,2,5,3] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
[-,4,2,5,3] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 2
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[-,4,+,2,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 2
[+,4,-,2,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 2
[+,4,+,2,-] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 2
[-,4,-,2,+] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[-,4,+,2,-] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[+,4,-,2,-] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[-,4,-,2,-] => [4,1,2,3,5] => [1,4] => ([(3,4)],5)
=> ? = 0 + 2
[+,4,+,5,2] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 2
[-,4,+,5,2] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[+,4,-,5,2] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 2
[+,5,2,+,3] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[+,5,+,2,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[3,+,1,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[4,1,+,2,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[4,+,1,3,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[4,+,+,1,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,1,2,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,1,+,2,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,1,+,+,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,+,1,3,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,+,1,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,+,+,1,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[5,+,+,+,1] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 0 + 2
[+,+,+,6,+,4] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,+,5,+,3,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,+,6,3,+,4] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,+,6,+,3,5] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,+,6,+,+,3] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,4,+,2,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,5,2,+,3,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,5,+,2,4,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,5,+,+,2,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,6,2,3,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,6,2,+,3,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,6,2,+,+,3] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,6,+,2,4,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,6,+,2,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,6,+,+,2,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[+,6,+,+,+,2] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[3,+,1,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[4,1,+,2,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[4,+,1,3,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[4,+,+,1,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[5,1,2,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[5,1,+,2,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[5,1,+,+,2,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[5,+,1,3,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[5,+,1,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[5,+,+,1,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[5,+,+,+,1,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
[6,1,2,3,+,4] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 0 + 2
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St000777
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 33%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 33%
Values
[3,+,1] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 3 = 0 + 3
[3,-,1] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? = 0 + 3
[+,4,+,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 0 + 3
[-,4,+,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[+,4,-,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[-,4,-,2] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 3
[2,1,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 3
[2,4,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 3
[2,4,+,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[2,4,-,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 3
[3,1,4,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 3
[3,+,1,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 0 + 3
[3,-,1,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[3,+,1,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[3,-,1,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 0 + 3
[3,+,4,1] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[3,-,4,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 3
[3,4,1,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 1 + 3
[3,4,2,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[4,1,+,2] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 0 + 3
[4,1,-,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[4,+,1,3] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 0 + 3
[4,-,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[4,+,+,1] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 0 + 3
[4,-,+,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[4,+,-,1] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[4,-,-,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 0 + 3
[4,3,1,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[4,3,2,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[+,+,5,+,3] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[-,+,5,+,3] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 3
[+,-,5,+,3] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 3
[+,+,5,-,3] => [1,2,5,3,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 3
[-,-,5,+,3] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 3
[-,+,5,-,3] => [2,5,1,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 3
[+,-,5,-,3] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 3
[-,-,5,-,3] => [5,1,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 0 + 3
[+,3,2,5,4] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 3
[-,3,2,5,4] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 3
[+,3,5,2,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 3
[-,3,5,2,4] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 3
[+,3,5,+,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 3
[-,3,5,+,2] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 3
[+,3,5,-,2] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 3
[-,3,5,-,2] => [5,1,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 0 + 3
[+,4,2,5,3] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 3
[-,4,2,5,3] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 3
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[-,4,+,2,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 3
[+,4,-,2,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 3
[+,4,+,2,-] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 3
[-,4,-,2,+] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 3
[-,4,+,2,-] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 3
[+,4,-,2,-] => [1,4,2,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 3
[-,4,-,2,-] => [4,1,2,3,5] => [1,4] => ([(3,4)],5)
=> ? = 0 + 3
[+,4,+,5,2] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 3
[-,4,+,5,2] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 3
[+,4,-,5,2] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 0 + 3
[+,5,2,+,3] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[+,5,+,2,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[3,+,1,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[4,1,+,2,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[4,+,1,3,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[4,+,+,1,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[5,1,2,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[5,1,+,2,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[5,1,+,+,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[5,+,1,3,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[5,+,1,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[5,+,+,1,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[5,+,+,+,1] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[+,+,+,6,+,4] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,+,5,+,3,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,+,6,3,+,4] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,+,6,+,3,5] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,+,6,+,+,3] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,4,+,2,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,5,2,+,3,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,5,+,2,4,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,5,+,+,2,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,6,2,3,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,6,2,+,3,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,6,2,+,+,3] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,6,+,2,4,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,6,+,2,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,6,+,+,2,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[+,6,+,+,+,2] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[3,+,1,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[4,1,+,2,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[4,+,1,3,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[4,+,+,1,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[5,1,2,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[5,1,+,2,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[5,1,+,+,2,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[5,+,1,3,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[5,+,1,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[5,+,+,1,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[5,+,+,+,1,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
[6,1,2,3,+,4] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 0 + 3
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St001768
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001768: Signed permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 67%
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001768: Signed permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 67%
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.
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