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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001569
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(load all 19 compositions to match this statistic)
Mp00255: Decorated permutations —lower permutation⟶ Permutations
St001569: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St001569: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+,+] => [1,2] => 0
[-,+] => [2,1] => 1
[+,-] => [1,2] => 0
[-,-] => [1,2] => 0
[2,1] => [1,2] => 0
[+,+,+] => [1,2,3] => 0
[-,+,+] => [2,3,1] => 1
[+,-,+] => [1,3,2] => 1
[+,+,-] => [1,2,3] => 0
[-,-,+] => [3,1,2] => 1
[-,+,-] => [2,1,3] => 1
[+,-,-] => [1,2,3] => 0
[-,-,-] => [1,2,3] => 0
[+,3,2] => [1,2,3] => 0
[-,3,2] => [2,1,3] => 1
[2,1,+] => [1,3,2] => 1
[2,1,-] => [1,2,3] => 0
[2,3,1] => [1,2,3] => 0
[3,1,2] => [1,2,3] => 0
[3,+,1] => [2,1,3] => 1
[3,-,1] => [1,3,2] => 1
[+,+,+,+] => [1,2,3,4] => 0
[-,+,+,+] => [2,3,4,1] => 1
[+,-,+,+] => [1,3,4,2] => 2
[+,+,-,+] => [1,2,4,3] => 1
[+,+,+,-] => [1,2,3,4] => 0
[-,-,+,+] => [3,4,1,2] => 2
[-,+,-,+] => [2,4,1,3] => 2
[-,+,+,-] => [2,3,1,4] => 2
[+,-,-,+] => [1,4,2,3] => 2
[+,-,+,-] => [1,3,2,4] => 1
[+,+,-,-] => [1,2,3,4] => 0
[-,-,-,+] => [4,1,2,3] => 1
[-,-,+,-] => [3,1,2,4] => 2
[-,+,-,-] => [2,1,3,4] => 1
[+,-,-,-] => [1,2,3,4] => 0
[-,-,-,-] => [1,2,3,4] => 0
[+,+,4,3] => [1,2,3,4] => 0
[-,+,4,3] => [2,3,1,4] => 2
[+,-,4,3] => [1,3,2,4] => 1
[-,-,4,3] => [3,1,2,4] => 2
[+,3,2,+] => [1,2,4,3] => 1
[-,3,2,+] => [2,4,1,3] => 2
[+,3,2,-] => [1,2,3,4] => 0
[-,3,2,-] => [2,1,3,4] => 1
[+,3,4,2] => [1,2,3,4] => 0
[-,3,4,2] => [2,1,3,4] => 1
[+,4,2,3] => [1,2,3,4] => 0
[-,4,2,3] => [2,3,1,4] => 2
[+,4,+,2] => [1,3,2,4] => 1
Description
The maximal modular displacement of a permutation.
This is $\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation $\pi$ of $\{1,\dots,n\}$.
Matching statistic: St000260
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(load all 2 compositions to match this statistic)
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 67%
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 67%
Values
[+,+] => [1,2] => ([],2)
=> ? = 0
[-,+] => [2,1] => ([(0,1)],2)
=> 1
[+,-] => [1,2] => ([],2)
=> ? = 0
[-,-] => [1,2] => ([],2)
=> ? = 0
[2,1] => [1,2] => ([],2)
=> ? = 0
[+,+,+] => [1,2,3] => ([],3)
=> ? = 0
[-,+,+] => [2,3,1] => ([(0,2),(1,2)],3)
=> 1
[+,-,+] => [1,3,2] => ([(1,2)],3)
=> ? = 1
[+,+,-] => [1,2,3] => ([],3)
=> ? = 0
[-,-,+] => [3,1,2] => ([(0,2),(1,2)],3)
=> 1
[-,+,-] => [2,1,3] => ([(1,2)],3)
=> ? = 1
[+,-,-] => [1,2,3] => ([],3)
=> ? = 0
[-,-,-] => [1,2,3] => ([],3)
=> ? = 0
[+,3,2] => [1,2,3] => ([],3)
=> ? = 0
[-,3,2] => [2,1,3] => ([(1,2)],3)
=> ? = 1
[2,1,+] => [1,3,2] => ([(1,2)],3)
=> ? = 1
[2,1,-] => [1,2,3] => ([],3)
=> ? = 0
[2,3,1] => [1,2,3] => ([],3)
=> ? = 0
[3,1,2] => [1,2,3] => ([],3)
=> ? = 0
[3,+,1] => [2,1,3] => ([(1,2)],3)
=> ? = 1
[3,-,1] => [1,3,2] => ([(1,2)],3)
=> ? = 1
[+,+,+,+] => [1,2,3,4] => ([],4)
=> ? = 0
[-,+,+,+] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[+,-,+,+] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,+,-,+] => [1,2,4,3] => ([(2,3)],4)
=> ? = 1
[+,+,+,-] => [1,2,3,4] => ([],4)
=> ? = 0
[-,-,+,+] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
[-,+,-,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 2
[-,+,+,-] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? = 2
[+,-,-,+] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? = 2
[+,-,+,-] => [1,3,2,4] => ([(2,3)],4)
=> ? = 1
[+,+,-,-] => [1,2,3,4] => ([],4)
=> ? = 0
[-,-,-,+] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,-,+,-] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? = 2
[-,+,-,-] => [2,1,3,4] => ([(2,3)],4)
=> ? = 1
[+,-,-,-] => [1,2,3,4] => ([],4)
=> ? = 0
[-,-,-,-] => [1,2,3,4] => ([],4)
=> ? = 0
[+,+,4,3] => [1,2,3,4] => ([],4)
=> ? = 0
[-,+,4,3] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? = 2
[+,-,4,3] => [1,3,2,4] => ([(2,3)],4)
=> ? = 1
[-,-,4,3] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? = 2
[+,3,2,+] => [1,2,4,3] => ([(2,3)],4)
=> ? = 1
[-,3,2,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> 2
[+,3,2,-] => [1,2,3,4] => ([],4)
=> ? = 0
[-,3,2,-] => [2,1,3,4] => ([(2,3)],4)
=> ? = 1
[+,3,4,2] => [1,2,3,4] => ([],4)
=> ? = 0
[-,3,4,2] => [2,1,3,4] => ([(2,3)],4)
=> ? = 1
[+,4,2,3] => [1,2,3,4] => ([],4)
=> ? = 0
[-,4,2,3] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? = 2
[+,4,+,2] => [1,3,2,4] => ([(2,3)],4)
=> ? = 1
[-,4,+,2] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? = 2
[+,4,-,2] => [1,2,4,3] => ([(2,3)],4)
=> ? = 1
[-,4,-,2] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? = 1
[2,1,+,+] => [1,3,4,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,1,-,+] => [1,4,2,3] => ([(1,3),(2,3)],4)
=> ? = 2
[2,1,+,-] => [1,3,2,4] => ([(2,3)],4)
=> ? = 1
[2,1,-,-] => [1,2,3,4] => ([],4)
=> ? = 0
[2,1,4,3] => [1,3,2,4] => ([(2,3)],4)
=> ? = 1
[4,-,+,1] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[-,+,+,+,+] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[-,-,+,+,+] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[-,+,-,+,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2
[-,+,+,-,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[-,-,-,+,+] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
[-,-,+,-,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2
[-,+,-,-,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[-,-,-,-,+] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[-,+,4,3,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[-,-,4,3,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2
[-,3,2,+,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2
[-,3,2,-,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[-,3,4,2,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[-,4,2,3,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[-,4,+,2,+] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[-,4,-,2,+] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[-,5,-,2,4] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[-,5,-,+,2] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[2,4,+,1,+] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[2,5,-,+,1] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[4,-,+,1,+] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[5,-,+,1,4] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 2
[5,-,+,+,1] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2
[5,+,-,+,1] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[5,-,-,+,1] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 2
[5,-,+,-,1] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[5,-,4,3,1] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[5,3,2,+,1] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
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