searching the database
Your data matches 8 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St001425
St001425: Decorated permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+] => 0
[-] => 1
[+,+] => 0
[-,+] => 1
[+,-] => 1
[-,-] => 2
[2,1] => 0
[+,+,+] => 0
[-,+,+] => 1
[+,-,+] => 1
[+,+,-] => 1
[-,-,+] => 2
[-,+,-] => 2
[+,-,-] => 2
[-,-,-] => 3
[+,3,2] => 0
[-,3,2] => 1
[2,1,+] => 0
[2,1,-] => 1
[2,3,1] => 0
[3,1,2] => 0
[3,+,1] => 0
[3,-,1] => 1
[+,+,+,+] => 0
[-,+,+,+] => 1
[+,-,+,+] => 1
[+,+,-,+] => 1
[+,+,+,-] => 1
[-,-,+,+] => 2
[-,+,-,+] => 2
[-,+,+,-] => 2
[+,-,-,+] => 2
[+,-,+,-] => 2
[+,+,-,-] => 2
[-,-,-,+] => 3
[-,-,+,-] => 3
[-,+,-,-] => 3
[+,-,-,-] => 3
[-,-,-,-] => 4
[+,+,4,3] => 0
[-,+,4,3] => 1
[+,-,4,3] => 1
[-,-,4,3] => 2
[+,3,2,+] => 0
[-,3,2,+] => 1
[+,3,2,-] => 1
[-,3,2,-] => 2
[+,3,4,2] => 0
[-,3,4,2] => 1
[+,4,2,3] => 0
Description
The number of negatively decorated fixed points of a decorated permutation.
Matching statistic: St001632
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 47% ●values known / values provided: 47%●distinct values known / distinct values provided: 50%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 47% ●values known / values provided: 47%●distinct values known / distinct values provided: 50%
Values
[+] => [1] => [1] => ([],1)
=> ? ∊ {0,1}
[-] => [1] => [1] => ([],1)
=> ? ∊ {0,1}
[+,+] => [1,2] => [2,1] => ([],2)
=> ? ∊ {0,0,1,2}
[-,+] => [1,2] => [2,1] => ([],2)
=> ? ∊ {0,0,1,2}
[+,-] => [1,2] => [2,1] => ([],2)
=> ? ∊ {0,0,1,2}
[-,-] => [1,2] => [2,1] => ([],2)
=> ? ∊ {0,0,1,2}
[2,1] => [2,1] => [1,2] => ([(0,1)],2)
=> 1
[+,+,+] => [1,2,3] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[-,+,+] => [1,2,3] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[+,-,+] => [1,2,3] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[+,+,-] => [1,2,3] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[-,-,+] => [1,2,3] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[-,+,-] => [1,2,3] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[+,-,-] => [1,2,3] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[-,-,-] => [1,2,3] => [2,3,1] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[+,3,2] => [1,3,2] => [3,2,1] => ([],3)
=> ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[-,3,2] => [1,3,2] => [3,2,1] => ([],3)
=> ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[2,1,+] => [2,1,3] => [1,3,2] => ([(0,1),(0,2)],3)
=> 2
[2,1,-] => [2,1,3] => [1,3,2] => ([(0,1),(0,2)],3)
=> 2
[2,3,1] => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 1
[3,1,2] => [3,1,2] => [3,1,2] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[3,+,1] => [3,2,1] => [2,1,3] => ([(0,2),(1,2)],3)
=> 1
[3,-,1] => [3,2,1] => [2,1,3] => ([(0,2),(1,2)],3)
=> 1
[+,+,+,+] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,+,+,+] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,-,+,+] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,+,-,+] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,+,+,-] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,-,+,+] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,+,-,+] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,+,+,-] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,-,-,+] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,-,+,-] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,+,-,-] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,-,-,+] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,-,+,-] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,+,-,-] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,-,-,-] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,-,-,-] => [1,2,3,4] => [2,3,4,1] => ([(1,2),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,+,4,3] => [1,2,4,3] => [2,4,3,1] => ([(1,2),(1,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,+,4,3] => [1,2,4,3] => [2,4,3,1] => ([(1,2),(1,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,-,4,3] => [1,2,4,3] => [2,4,3,1] => ([(1,2),(1,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,-,4,3] => [1,2,4,3] => [2,4,3,1] => ([(1,2),(1,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,3,2,+] => [1,3,2,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,3,2,+] => [1,3,2,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,3,2,-] => [1,3,2,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,3,2,-] => [1,3,2,4] => [3,2,4,1] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,3,4,2] => [1,3,4,2] => [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,3,4,2] => [1,3,4,2] => [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,4,2,3] => [1,4,2,3] => [3,4,2,1] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,4,2,3] => [1,4,2,3] => [3,4,2,1] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,4,+,2] => [1,4,3,2] => [4,3,2,1] => ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,4,+,2] => [1,4,3,2] => [4,3,2,1] => ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[+,4,-,2] => [1,4,3,2] => [4,3,2,1] => ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[-,4,-,2] => [1,4,3,2] => [4,3,2,1] => ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[2,1,+,+] => [2,1,3,4] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> 2
[2,1,-,+] => [2,1,3,4] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> 2
[2,1,+,-] => [2,1,3,4] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> 2
[2,1,-,-] => [2,1,3,4] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> 2
[2,1,4,3] => [2,1,4,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> 0
[2,3,1,+] => [2,3,1,4] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> 1
[2,3,1,-] => [2,3,1,4] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> 1
[2,3,4,1] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[2,4,1,3] => [2,4,1,3] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> 2
[2,4,+,1] => [2,4,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[2,4,-,1] => [2,4,3,1] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[3,1,2,+] => [3,1,2,4] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> 0
[3,1,2,-] => [3,1,2,4] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> 0
[3,1,4,2] => [3,1,4,2] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4}
[3,+,1,+] => [3,2,1,4] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 0
[3,-,1,+] => [3,2,1,4] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 0
[3,+,1,-] => [3,2,1,4] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 0
[3,-,1,-] => [3,2,1,4] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 0
[3,+,4,1] => [3,2,4,1] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> 1
[3,-,4,1] => [3,2,4,1] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> 1
[3,4,2,1] => [3,4,2,1] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> 1
[4,+,1,3] => [4,2,1,3] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
=> 0
[4,-,1,3] => [4,2,1,3] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
=> 0
[4,+,+,1] => [4,2,3,1] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> 1
[4,-,+,1] => [4,2,3,1] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> 1
[4,+,-,1] => [4,2,3,1] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> 1
[4,-,-,1] => [4,2,3,1] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> 1
[4,3,2,1] => [4,3,2,1] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> 0
[2,1,+,+,+] => [2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> 2
[2,1,-,+,+] => [2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> 2
[2,1,+,-,+] => [2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> 2
[2,1,+,+,-] => [2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> 2
[2,1,-,-,+] => [2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> 2
[2,1,-,+,-] => [2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> 2
[2,1,+,-,-] => [2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> 2
[2,1,-,-,-] => [2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> 2
[2,1,+,5,4] => [2,1,3,5,4] => [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> 1
[2,1,-,5,4] => [2,1,3,5,4] => [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> 1
[2,1,4,3,+] => [2,1,4,3,5] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> 1
[2,1,4,3,-] => [2,1,4,3,5] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> 1
[2,1,4,5,3] => [2,1,4,5,3] => [1,5,3,4,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> 0
[2,1,5,3,4] => [2,1,5,3,4] => [1,4,5,3,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> 0
[2,1,5,+,3] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
=> 0
[2,1,5,-,3] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
=> 0
[2,3,1,+,+] => [2,3,1,4,5] => [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> 1
Description
The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset.
Matching statistic: St001491
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 36% ●values known / values provided: 36%●distinct values known / distinct values provided: 83%
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 36% ●values known / values provided: 36%●distinct values known / distinct values provided: 83%
Values
[+] => [1] => [1] => => ? ∊ {0,1}
[-] => [1] => [1] => => ? ∊ {0,1}
[+,+] => [1,2] => [2,1] => 0 => ? ∊ {0,0,1,2}
[-,+] => [1,2] => [2,1] => 0 => ? ∊ {0,0,1,2}
[+,-] => [1,2] => [2,1] => 0 => ? ∊ {0,0,1,2}
[-,-] => [1,2] => [2,1] => 0 => ? ∊ {0,0,1,2}
[2,1] => [2,1] => [1,2] => 1 => 1
[+,+,+] => [1,2,3] => [2,3,1] => 00 => ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[-,+,+] => [1,2,3] => [2,3,1] => 00 => ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[+,-,+] => [1,2,3] => [2,3,1] => 00 => ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[+,+,-] => [1,2,3] => [2,3,1] => 00 => ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[-,-,+] => [1,2,3] => [2,3,1] => 00 => ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[-,+,-] => [1,2,3] => [2,3,1] => 00 => ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[+,-,-] => [1,2,3] => [2,3,1] => 00 => ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[-,-,-] => [1,2,3] => [2,3,1] => 00 => ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[+,3,2] => [1,3,2] => [2,1,3] => 01 => 1
[-,3,2] => [1,3,2] => [2,1,3] => 01 => 1
[2,1,+] => [2,1,3] => [3,2,1] => 00 => ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[2,1,-] => [2,1,3] => [3,2,1] => 00 => ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[2,3,1] => [2,3,1] => [3,1,2] => 00 => ? ∊ {0,0,0,0,0,0,1,1,1,2,3}
[3,1,2] => [3,1,2] => [1,3,2] => 10 => 1
[3,+,1] => [3,2,1] => [1,2,3] => 11 => 2
[3,-,1] => [3,2,1] => [1,2,3] => 11 => 2
[+,+,+,+] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[-,+,+,+] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[+,-,+,+] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[+,+,-,+] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[+,+,+,-] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[-,-,+,+] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[-,+,-,+] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[-,+,+,-] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[+,-,-,+] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[+,-,+,-] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[+,+,-,-] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[-,-,-,+] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[-,-,+,-] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[-,+,-,-] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[+,-,-,-] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[-,-,-,-] => [1,2,3,4] => [2,3,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[+,+,4,3] => [1,2,4,3] => [2,3,1,4] => 001 => 1
[-,+,4,3] => [1,2,4,3] => [2,3,1,4] => 001 => 1
[+,-,4,3] => [1,2,4,3] => [2,3,1,4] => 001 => 1
[-,-,4,3] => [1,2,4,3] => [2,3,1,4] => 001 => 1
[+,3,2,+] => [1,3,2,4] => [2,4,3,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[-,3,2,+] => [1,3,2,4] => [2,4,3,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[+,3,2,-] => [1,3,2,4] => [2,4,3,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[-,3,2,-] => [1,3,2,4] => [2,4,3,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[+,3,4,2] => [1,3,4,2] => [2,4,1,3] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[-,3,4,2] => [1,3,4,2] => [2,4,1,3] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[+,4,2,3] => [1,4,2,3] => [2,1,4,3] => 010 => 1
[-,4,2,3] => [1,4,2,3] => [2,1,4,3] => 010 => 1
[+,4,+,2] => [1,4,3,2] => [2,1,3,4] => 011 => 1
[-,4,+,2] => [1,4,3,2] => [2,1,3,4] => 011 => 1
[+,4,-,2] => [1,4,3,2] => [2,1,3,4] => 011 => 1
[-,4,-,2] => [1,4,3,2] => [2,1,3,4] => 011 => 1
[2,1,+,+] => [2,1,3,4] => [3,2,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[2,1,-,+] => [2,1,3,4] => [3,2,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[2,1,+,-] => [2,1,3,4] => [3,2,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[2,1,-,-] => [2,1,3,4] => [3,2,4,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[2,1,4,3] => [2,1,4,3] => [3,2,1,4] => 001 => 1
[2,3,1,+] => [2,3,1,4] => [3,4,2,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[2,3,1,-] => [2,3,1,4] => [3,4,2,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[2,3,4,1] => [2,3,4,1] => [3,4,1,2] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[2,4,1,3] => [2,4,1,3] => [3,1,4,2] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[2,4,+,1] => [2,4,3,1] => [3,1,2,4] => 001 => 1
[2,4,-,1] => [2,4,3,1] => [3,1,2,4] => 001 => 1
[3,1,2,+] => [3,1,2,4] => [4,2,3,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[3,1,2,-] => [3,1,2,4] => [4,2,3,1] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[3,1,4,2] => [3,1,4,2] => [4,2,1,3] => 000 => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,4}
[4,1,2,3] => [4,1,2,3] => [1,3,4,2] => 100 => 1
[4,1,+,2] => [4,1,3,2] => [1,3,2,4] => 101 => 2
[4,1,-,2] => [4,1,3,2] => [1,3,2,4] => 101 => 2
[4,+,1,3] => [4,2,1,3] => [1,4,3,2] => 100 => 1
[4,-,1,3] => [4,2,1,3] => [1,4,3,2] => 100 => 1
[4,+,+,1] => [4,2,3,1] => [1,4,2,3] => 100 => 1
[4,-,+,1] => [4,2,3,1] => [1,4,2,3] => 100 => 1
[4,+,-,1] => [4,2,3,1] => [1,4,2,3] => 100 => 1
[4,-,-,1] => [4,2,3,1] => [1,4,2,3] => 100 => 1
[4,3,1,2] => [4,3,1,2] => [1,2,4,3] => 110 => 1
[4,3,2,1] => [4,3,2,1] => [1,2,3,4] => 111 => 3
[+,+,+,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => 0001 => 1
[-,+,+,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => 0001 => 1
[+,-,+,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => 0001 => 1
[+,+,-,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => 0001 => 1
[-,-,+,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => 0001 => 1
[-,+,-,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => 0001 => 1
[+,-,-,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => 0001 => 1
[-,-,-,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => 0001 => 1
[+,+,5,3,4] => [1,2,5,3,4] => [2,3,1,5,4] => 0010 => 1
[-,+,5,3,4] => [1,2,5,3,4] => [2,3,1,5,4] => 0010 => 1
[+,-,5,3,4] => [1,2,5,3,4] => [2,3,1,5,4] => 0010 => 1
[-,-,5,3,4] => [1,2,5,3,4] => [2,3,1,5,4] => 0010 => 1
[+,+,5,+,3] => [1,2,5,4,3] => [2,3,1,4,5] => 0011 => 1
[-,+,5,+,3] => [1,2,5,4,3] => [2,3,1,4,5] => 0011 => 1
[+,-,5,+,3] => [1,2,5,4,3] => [2,3,1,4,5] => 0011 => 1
[+,+,5,-,3] => [1,2,5,4,3] => [2,3,1,4,5] => 0011 => 1
[-,-,5,+,3] => [1,2,5,4,3] => [2,3,1,4,5] => 0011 => 1
[-,+,5,-,3] => [1,2,5,4,3] => [2,3,1,4,5] => 0011 => 1
[+,-,5,-,3] => [1,2,5,4,3] => [2,3,1,4,5] => 0011 => 1
[-,-,5,-,3] => [1,2,5,4,3] => [2,3,1,4,5] => 0011 => 1
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset.
Let $A_n=K[x]/(x^n)$.
We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.
Matching statistic: St001629
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St001629: Integer compositions ⟶ ℤResult quality: 28% ●values known / values provided: 28%●distinct values known / distinct values provided: 33%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St001629: Integer compositions ⟶ ℤResult quality: 28% ●values known / values provided: 28%●distinct values known / distinct values provided: 33%
Values
[+] => [1] => [1] => [1] => ? ∊ {0,1}
[-] => [1] => [1] => [1] => ? ∊ {0,1}
[+,+] => [1,2] => [2] => [1] => ? ∊ {0,0,1,1,2}
[-,+] => [2,1] => [1,1] => [2] => ? ∊ {0,0,1,1,2}
[+,-] => [1,2] => [2] => [1] => ? ∊ {0,0,1,1,2}
[-,-] => [1,2] => [2] => [1] => ? ∊ {0,0,1,1,2}
[2,1] => [1,2] => [2] => [1] => ? ∊ {0,0,1,1,2}
[+,+,+] => [1,2,3] => [3] => [1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,+,+] => [2,3,1] => [2,1] => [1,1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,-,+] => [1,3,2] => [2,1] => [1,1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,+,-] => [1,2,3] => [3] => [1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,-,+] => [3,1,2] => [1,2] => [1,1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,+,-] => [2,1,3] => [1,2] => [1,1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,-,-] => [1,2,3] => [3] => [1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,-,-] => [1,2,3] => [3] => [1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,3,2] => [1,2,3] => [3] => [1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,3,2] => [2,1,3] => [1,2] => [1,1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[2,1,+] => [1,3,2] => [2,1] => [1,1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[2,1,-] => [1,2,3] => [3] => [1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[2,3,1] => [1,2,3] => [3] => [1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[3,1,2] => [1,2,3] => [3] => [1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[3,+,1] => [2,1,3] => [1,2] => [1,1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[3,-,1] => [1,3,2] => [2,1] => [1,1] => ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,+,+,+] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,+,+] => [2,3,4,1] => [3,1] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,+,+] => [1,3,4,2] => [3,1] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,-,+] => [1,2,4,3] => [3,1] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,+,-] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,+,+] => [3,4,1,2] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,-,+] => [2,4,1,3] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,+,-] => [2,3,1,4] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,-,+] => [1,4,2,3] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,+,-] => [1,3,2,4] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,-,-] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,-,+] => [4,1,2,3] => [1,3] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,+,-] => [3,1,2,4] => [1,3] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,-,-] => [2,1,3,4] => [1,3] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,-,-] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,-,-] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,4,3] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,4,3] => [2,3,1,4] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,4,3] => [1,3,2,4] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,4,3] => [3,1,2,4] => [1,3] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,3,2,+] => [1,2,4,3] => [3,1] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,3,2,+] => [2,4,1,3] => [2,2] => [2] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,3,2,-] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,3,2,-] => [2,1,3,4] => [1,3] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,3,4,2] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,3,4,2] => [2,1,3,4] => [1,3] => [1,1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,4,2,3] => [1,2,3,4] => [4] => [1] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,4,+,2] => [3,2,1,4] => [1,1,2] => [2,1] => 0
[-,4,-,2] => [2,1,4,3] => [1,2,1] => [1,1,1] => 1
[3,+,1,+] => [2,1,4,3] => [1,2,1] => [1,1,1] => 1
[3,-,1,+] => [1,4,3,2] => [2,1,1] => [1,2] => 0
[4,-,+,1] => [3,1,4,2] => [1,2,1] => [1,1,1] => 1
[4,+,-,1] => [2,1,4,3] => [1,2,1] => [1,1,1] => 1
[4,3,2,1] => [2,1,4,3] => [1,2,1] => [1,1,1] => 1
[-,+,5,+,3] => [2,4,3,1,5] => [2,1,2] => [1,1,1] => 1
[+,-,5,+,3] => [1,4,3,2,5] => [2,1,2] => [1,1,1] => 1
[-,-,5,+,3] => [4,3,1,2,5] => [1,1,3] => [2,1] => 0
[-,+,5,-,3] => [2,3,1,5,4] => [2,2,1] => [2,1] => 0
[+,-,5,-,3] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[-,-,5,-,3] => [3,1,2,5,4] => [1,3,1] => [1,1,1] => 1
[-,3,5,+,2] => [4,2,1,3,5] => [1,1,3] => [2,1] => 0
[-,3,5,-,2] => [2,1,3,5,4] => [1,3,1] => [1,1,1] => 1
[+,4,+,2,+] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[-,4,+,2,+] => [3,2,5,1,4] => [1,2,2] => [1,2] => 0
[+,4,-,2,+] => [1,2,5,4,3] => [3,1,1] => [1,2] => 0
[-,4,-,2,+] => [2,5,1,4,3] => [2,2,1] => [2,1] => 0
[-,4,+,2,-] => [3,2,1,4,5] => [1,1,3] => [2,1] => 0
[-,4,-,2,-] => [2,1,4,3,5] => [1,2,2] => [1,2] => 0
[-,4,+,5,2] => [3,2,1,4,5] => [1,1,3] => [2,1] => 0
[-,4,-,5,2] => [2,1,4,3,5] => [1,2,2] => [1,2] => 0
[-,4,5,3,2] => [3,2,1,4,5] => [1,1,3] => [2,1] => 0
[-,5,2,+,3] => [2,4,3,1,5] => [2,1,2] => [1,1,1] => 1
[-,5,2,-,3] => [2,3,1,5,4] => [2,2,1] => [2,1] => 0
[-,5,+,2,4] => [3,2,4,1,5] => [1,2,2] => [1,2] => 0
[-,5,-,2,4] => [2,4,1,5,3] => [2,2,1] => [2,1] => 0
[-,5,+,+,2] => [3,4,2,1,5] => [2,1,2] => [1,1,1] => 1
[+,5,-,+,2] => [1,4,2,5,3] => [2,2,1] => [2,1] => 0
[+,5,+,-,2] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[-,5,-,+,2] => [4,2,1,5,3] => [1,1,2,1] => [2,1,1] => 1
[-,5,+,-,2] => [3,2,1,5,4] => [1,1,2,1] => [2,1,1] => 1
[-,5,-,-,2] => [2,1,5,3,4] => [1,2,2] => [1,2] => 0
[-,5,4,2,3] => [2,3,1,5,4] => [2,2,1] => [2,1] => 0
[+,5,4,3,2] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[-,5,4,3,2] => [3,2,1,5,4] => [1,1,2,1] => [2,1,1] => 1
[2,1,5,+,3] => [1,4,3,2,5] => [2,1,2] => [1,1,1] => 1
[2,1,5,-,3] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[2,4,+,1,+] => [3,1,5,2,4] => [1,2,2] => [1,2] => 0
[2,4,-,1,+] => [1,5,2,4,3] => [2,2,1] => [2,1] => 0
[2,5,1,+,3] => [1,4,3,2,5] => [2,1,2] => [1,1,1] => 1
[2,5,1,-,3] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[2,5,+,1,4] => [3,1,4,2,5] => [1,2,2] => [1,2] => 0
[2,5,-,1,4] => [1,4,2,5,3] => [2,2,1] => [2,1] => 0
[2,5,-,+,1] => [4,1,2,5,3] => [1,3,1] => [1,1,1] => 1
[2,5,+,-,1] => [3,1,2,5,4] => [1,3,1] => [1,1,1] => 1
[2,5,4,1,3] => [1,3,2,5,4] => [2,2,1] => [2,1] => 0
[2,5,4,3,1] => [3,1,2,5,4] => [1,3,1] => [1,1,1] => 1
[3,+,1,+,+] => [2,1,4,5,3] => [1,3,1] => [1,1,1] => 1
Description
The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.
Matching statistic: St001426
St001426: Decorated permutations ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 83%
Values
[+] => 1
[-] => 0
[+,+] => 2
[-,+] => 1
[+,-] => 1
[-,-] => 0
[2,1] => 0
[+,+,+] => 3
[-,+,+] => 2
[+,-,+] => 2
[+,+,-] => 2
[-,-,+] => 1
[-,+,-] => 1
[+,-,-] => 1
[-,-,-] => 0
[+,3,2] => 1
[-,3,2] => 0
[2,1,+] => 1
[2,1,-] => 0
[2,3,1] => 0
[3,1,2] => 0
[3,+,1] => 1
[3,-,1] => 0
[+,+,+,+] => 4
[-,+,+,+] => 3
[+,-,+,+] => 3
[+,+,-,+] => 3
[+,+,+,-] => 3
[-,-,+,+] => 2
[-,+,-,+] => 2
[-,+,+,-] => 2
[+,-,-,+] => 2
[+,-,+,-] => 2
[+,+,-,-] => 2
[-,-,-,+] => 1
[-,-,+,-] => 1
[-,+,-,-] => 1
[+,-,-,-] => 1
[-,-,-,-] => 0
[+,+,4,3] => 2
[-,+,4,3] => 1
[+,-,4,3] => 1
[-,-,4,3] => 0
[+,3,2,+] => 2
[-,3,2,+] => 1
[+,3,2,-] => 1
[-,3,2,-] => 0
[+,3,4,2] => 1
[-,3,4,2] => 0
[+,4,2,3] => 1
[+,+,+,+,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,+,+,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,-,+,+,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,+,-,+,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,+,+,-,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,+,+,+,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,-,+,+,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,-,+,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,+,-,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,+,+,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,-,-,+,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,-,+,-,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,-,+,+,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,+,-,-,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,+,-,+,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,+,+,-,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,-,-,+,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,-,+,-,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,-,+,+,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,-,-,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,-,+,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,+,-,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,-,-,-,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,-,-,+,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,-,+,-,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,+,-,-,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,-,-,-,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,-,-,+,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,-,+,-,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,-,-,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,-,-,-,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,-,-,-,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,+,+,5,4] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,+,5,4] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,-,+,5,4] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,+,-,5,4] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,-,+,5,4] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,-,5,4] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,-,-,5,4] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,-,-,5,4] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,+,4,3,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,4,3,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,-,4,3,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,+,4,3,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,-,4,3,+] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,4,3,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,-,4,3,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,-,4,3,-] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[+,+,4,5,3] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
[-,+,4,5,3] => ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5}
Description
The number of positively decorated fixed points of a decorated permutation.
Matching statistic: St001603
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 33%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 33%
Values
[+] => [1] => [1]
=> []
=> ? ∊ {0,1}
[-] => [1] => [1]
=> []
=> ? ∊ {0,1}
[+,+] => [1,2] => [2]
=> []
=> ? ∊ {0,0,1,1,2}
[-,+] => [1,2] => [2]
=> []
=> ? ∊ {0,0,1,1,2}
[+,-] => [1,2] => [2]
=> []
=> ? ∊ {0,0,1,1,2}
[-,-] => [1,2] => [2]
=> []
=> ? ∊ {0,0,1,1,2}
[2,1] => [2,1] => [1,1]
=> [1]
=> ? ∊ {0,0,1,1,2}
[+,+,+] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,+,+] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,-,+] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,+,-] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,-,+] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,+,-] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,-,-] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,-,-] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[2,1,+] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[2,1,-] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[2,3,1] => [2,3,1] => [2,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[3,1,2] => [3,1,2] => [2,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[3,+,1] => [3,2,1] => [1,1,1]
=> [1,1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[3,-,1] => [3,2,1] => [1,1,1]
=> [1,1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,+,+,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,+,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,+,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,-,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,+,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,+,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,-,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,+,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,-,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,+,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,-,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,-,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,+,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,-,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,-,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,-,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,3,2,+] => [1,3,2,4] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,3,2,+] => [1,3,2,4] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,3,2,-] => [1,3,2,4] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,3,2,-] => [1,3,2,4] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,3,4,2] => [1,3,4,2] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,3,4,2] => [1,3,4,2] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,4,2,3] => [1,4,2,3] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[4,3,2,1] => [4,3,2,1] => [1,1,1,1]
=> [1,1,1]
=> 1
[+,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
=> [1,1,1]
=> 1
[-,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
=> [1,1,1]
=> 1
[2,1,5,+,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 1
[2,1,5,-,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 1
[2,5,1,+,3] => [2,5,1,4,3] => [2,2,1]
=> [2,1]
=> 1
[2,5,1,-,3] => [2,5,1,4,3] => [2,2,1]
=> [2,1]
=> 1
[2,5,4,1,3] => [2,5,4,1,3] => [2,2,1]
=> [2,1]
=> 1
[2,5,4,3,1] => [2,5,4,3,1] => [2,1,1,1]
=> [1,1,1]
=> 1
[3,1,5,+,2] => [3,1,5,4,2] => [2,2,1]
=> [2,1]
=> 1
[3,1,5,-,2] => [3,1,5,4,2] => [2,2,1]
=> [2,1]
=> 1
[3,+,1,5,4] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 1
[3,-,1,5,4] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 1
[3,+,5,1,4] => [3,2,5,1,4] => [2,2,1]
=> [2,1]
=> 1
[3,-,5,1,4] => [3,2,5,1,4] => [2,2,1]
=> [2,1]
=> 1
[3,+,5,+,1] => [3,2,5,4,1] => [2,2,1]
=> [2,1]
=> 1
[3,-,5,+,1] => [3,2,5,4,1] => [2,2,1]
=> [2,1]
=> 1
[3,+,5,-,1] => [3,2,5,4,1] => [2,2,1]
=> [2,1]
=> 1
[3,-,5,-,1] => [3,2,5,4,1] => [2,2,1]
=> [2,1]
=> 1
[3,5,1,+,2] => [3,5,1,4,2] => [2,2,1]
=> [2,1]
=> 1
[3,5,1,-,2] => [3,5,1,4,2] => [2,2,1]
=> [2,1]
=> 1
[3,5,2,1,4] => [3,5,2,1,4] => [2,2,1]
=> [2,1]
=> 1
[3,5,2,+,1] => [3,5,2,4,1] => [2,2,1]
=> [2,1]
=> 1
[3,5,2,-,1] => [3,5,2,4,1] => [2,2,1]
=> [2,1]
=> 1
[3,5,4,1,2] => [3,5,4,1,2] => [2,2,1]
=> [2,1]
=> 1
[3,5,4,2,1] => [3,5,4,2,1] => [2,1,1,1]
=> [1,1,1]
=> 1
[4,1,5,3,2] => [4,1,5,3,2] => [2,2,1]
=> [2,1]
=> 1
[4,+,1,5,3] => [4,2,1,5,3] => [2,2,1]
=> [2,1]
=> 1
[4,-,1,5,3] => [4,2,1,5,3] => [2,2,1]
=> [2,1]
=> 1
[4,+,5,1,3] => [4,2,5,1,3] => [2,2,1]
=> [2,1]
=> 1
[4,-,5,1,3] => [4,2,5,1,3] => [2,2,1]
=> [2,1]
=> 1
[4,+,5,3,1] => [4,2,5,3,1] => [2,2,1]
=> [2,1]
=> 1
[4,-,5,3,1] => [4,2,5,3,1] => [2,2,1]
=> [2,1]
=> 1
[4,3,1,5,2] => [4,3,1,5,2] => [2,2,1]
=> [2,1]
=> 1
[4,3,2,1,+] => [4,3,2,1,5] => [2,1,1,1]
=> [1,1,1]
=> 1
[4,3,2,1,-] => [4,3,2,1,5] => [2,1,1,1]
=> [1,1,1]
=> 1
[4,3,2,5,1] => [4,3,2,5,1] => [2,1,1,1]
=> [1,1,1]
=> 1
[4,3,5,1,2] => [4,3,5,1,2] => [2,2,1]
=> [2,1]
=> 1
[4,3,5,2,1] => [4,3,5,2,1] => [2,1,1,1]
=> [1,1,1]
=> 1
[4,5,1,3,2] => [4,5,1,3,2] => [2,2,1]
=> [2,1]
=> 1
[4,5,2,1,3] => [4,5,2,1,3] => [2,2,1]
=> [2,1]
=> 1
[4,5,2,3,1] => [4,5,2,3,1] => [2,2,1]
=> [2,1]
=> 1
[4,5,+,1,2] => [4,5,3,1,2] => [2,2,1]
=> [2,1]
=> 1
[4,5,-,1,2] => [4,5,3,1,2] => [2,2,1]
=> [2,1]
=> 1
[4,5,+,2,1] => [4,5,3,2,1] => [2,1,1,1]
=> [1,1,1]
=> 1
[4,5,-,2,1] => [4,5,3,2,1] => [2,1,1,1]
=> [1,1,1]
=> 1
[5,1,4,3,2] => [5,1,4,3,2] => [2,1,1,1]
=> [1,1,1]
=> 1
[5,+,1,+,3] => [5,2,1,4,3] => [2,2,1]
=> [2,1]
=> 1
[5,-,1,+,3] => [5,2,1,4,3] => [2,2,1]
=> [2,1]
=> 1
[5,+,1,-,3] => [5,2,1,4,3] => [2,2,1]
=> [2,1]
=> 1
Description
The number of colourings of a polygon such that the multiplicities of a colour are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001604
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 17%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 17%
Values
[+] => [1] => [1]
=> []
=> ? ∊ {0,1}
[-] => [1] => [1]
=> []
=> ? ∊ {0,1}
[+,+] => [1,2] => [2]
=> []
=> ? ∊ {0,0,1,1,2}
[-,+] => [1,2] => [2]
=> []
=> ? ∊ {0,0,1,1,2}
[+,-] => [1,2] => [2]
=> []
=> ? ∊ {0,0,1,1,2}
[-,-] => [1,2] => [2]
=> []
=> ? ∊ {0,0,1,1,2}
[2,1] => [2,1] => [1,1]
=> [1]
=> ? ∊ {0,0,1,1,2}
[+,+,+] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,+,+] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,-,+] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,+,-] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,-,+] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,+,-] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,-,-] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,-,-] => [1,2,3] => [3]
=> []
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[-,3,2] => [1,3,2] => [2,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[2,1,+] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[2,1,-] => [2,1,3] => [2,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[2,3,1] => [2,3,1] => [2,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[3,1,2] => [3,1,2] => [2,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[3,+,1] => [3,2,1] => [1,1,1]
=> [1,1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[3,-,1] => [3,2,1] => [1,1,1]
=> [1,1]
=> ? ∊ {0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,3}
[+,+,+,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,+,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,+,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,-,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,+,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,+,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,-,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,+,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,-,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,+,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,-,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,-,+] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,+,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,-,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,-,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,-,-] => [1,2,3,4] => [4]
=> []
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,4,3] => [1,2,4,3] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,3,2,+] => [1,3,2,4] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,3,2,+] => [1,3,2,4] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,3,2,-] => [1,3,2,4] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,3,2,-] => [1,3,2,4] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,3,4,2] => [1,3,4,2] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,3,4,2] => [1,3,4,2] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,4,2,3] => [1,4,2,3] => [3,1]
=> [1]
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[4,3,2,1] => [4,3,2,1] => [1,1,1,1]
=> [1,1,1]
=> 0
[+,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
=> [1,1,1]
=> 0
[-,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1]
=> [1,1,1]
=> 0
[2,1,5,+,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 0
[2,1,5,-,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 0
[2,5,1,+,3] => [2,5,1,4,3] => [2,2,1]
=> [2,1]
=> 0
[2,5,1,-,3] => [2,5,1,4,3] => [2,2,1]
=> [2,1]
=> 0
[2,5,4,1,3] => [2,5,4,1,3] => [2,2,1]
=> [2,1]
=> 0
[2,5,4,3,1] => [2,5,4,3,1] => [2,1,1,1]
=> [1,1,1]
=> 0
[3,1,5,+,2] => [3,1,5,4,2] => [2,2,1]
=> [2,1]
=> 0
[3,1,5,-,2] => [3,1,5,4,2] => [2,2,1]
=> [2,1]
=> 0
[3,+,1,5,4] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 0
[3,-,1,5,4] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 0
[3,+,5,1,4] => [3,2,5,1,4] => [2,2,1]
=> [2,1]
=> 0
[3,-,5,1,4] => [3,2,5,1,4] => [2,2,1]
=> [2,1]
=> 0
[3,+,5,+,1] => [3,2,5,4,1] => [2,2,1]
=> [2,1]
=> 0
[3,-,5,+,1] => [3,2,5,4,1] => [2,2,1]
=> [2,1]
=> 0
[3,+,5,-,1] => [3,2,5,4,1] => [2,2,1]
=> [2,1]
=> 0
[3,-,5,-,1] => [3,2,5,4,1] => [2,2,1]
=> [2,1]
=> 0
[3,5,1,+,2] => [3,5,1,4,2] => [2,2,1]
=> [2,1]
=> 0
[3,5,1,-,2] => [3,5,1,4,2] => [2,2,1]
=> [2,1]
=> 0
[3,5,2,1,4] => [3,5,2,1,4] => [2,2,1]
=> [2,1]
=> 0
[3,5,2,+,1] => [3,5,2,4,1] => [2,2,1]
=> [2,1]
=> 0
[3,5,2,-,1] => [3,5,2,4,1] => [2,2,1]
=> [2,1]
=> 0
[3,5,4,1,2] => [3,5,4,1,2] => [2,2,1]
=> [2,1]
=> 0
[3,5,4,2,1] => [3,5,4,2,1] => [2,1,1,1]
=> [1,1,1]
=> 0
[4,1,5,3,2] => [4,1,5,3,2] => [2,2,1]
=> [2,1]
=> 0
[4,+,1,5,3] => [4,2,1,5,3] => [2,2,1]
=> [2,1]
=> 0
[4,-,1,5,3] => [4,2,1,5,3] => [2,2,1]
=> [2,1]
=> 0
[4,+,5,1,3] => [4,2,5,1,3] => [2,2,1]
=> [2,1]
=> 0
[4,-,5,1,3] => [4,2,5,1,3] => [2,2,1]
=> [2,1]
=> 0
[4,+,5,3,1] => [4,2,5,3,1] => [2,2,1]
=> [2,1]
=> 0
[4,-,5,3,1] => [4,2,5,3,1] => [2,2,1]
=> [2,1]
=> 0
[4,3,1,5,2] => [4,3,1,5,2] => [2,2,1]
=> [2,1]
=> 0
[4,3,2,1,+] => [4,3,2,1,5] => [2,1,1,1]
=> [1,1,1]
=> 0
[4,3,2,1,-] => [4,3,2,1,5] => [2,1,1,1]
=> [1,1,1]
=> 0
[4,3,2,5,1] => [4,3,2,5,1] => [2,1,1,1]
=> [1,1,1]
=> 0
[4,3,5,1,2] => [4,3,5,1,2] => [2,2,1]
=> [2,1]
=> 0
[4,3,5,2,1] => [4,3,5,2,1] => [2,1,1,1]
=> [1,1,1]
=> 0
[4,5,1,3,2] => [4,5,1,3,2] => [2,2,1]
=> [2,1]
=> 0
[4,5,2,1,3] => [4,5,2,1,3] => [2,2,1]
=> [2,1]
=> 0
[4,5,2,3,1] => [4,5,2,3,1] => [2,2,1]
=> [2,1]
=> 0
[4,5,+,1,2] => [4,5,3,1,2] => [2,2,1]
=> [2,1]
=> 0
[4,5,-,1,2] => [4,5,3,1,2] => [2,2,1]
=> [2,1]
=> 0
[4,5,+,2,1] => [4,5,3,2,1] => [2,1,1,1]
=> [1,1,1]
=> 0
[4,5,-,2,1] => [4,5,3,2,1] => [2,1,1,1]
=> [1,1,1]
=> 0
[5,1,4,3,2] => [5,1,4,3,2] => [2,1,1,1]
=> [1,1,1]
=> 0
[5,+,1,+,3] => [5,2,1,4,3] => [2,2,1]
=> [2,1]
=> 0
[5,-,1,+,3] => [5,2,1,4,3] => [2,2,1]
=> [2,1]
=> 0
[5,+,1,-,3] => [5,2,1,4,3] => [2,2,1]
=> [2,1]
=> 0
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons.
Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St000456
(load all 4 compositions to match this statistic)
(load all 4 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: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 17%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 17%
Values
[+] => [1] => [1] => ([],1)
=> ? ∊ {0,1}
[-] => [1] => [1] => ([],1)
=> ? ∊ {0,1}
[+,+] => [1,2] => [2] => ([],2)
=> ? ∊ {0,0,2}
[-,+] => [2,1] => [1,1] => ([(0,1)],2)
=> 1
[+,-] => [1,2] => [2] => ([],2)
=> ? ∊ {0,0,2}
[-,-] => [1,2] => [2] => ([],2)
=> ? ∊ {0,0,2}
[2,1] => [2,1] => [1,1] => ([(0,1)],2)
=> 1
[+,+,+] => [1,2,3] => [3] => ([],3)
=> ? ∊ {0,0,0,0,0,0,2,2,2,3}
[-,+,+] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[+,-,+] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[+,+,-] => [1,2,3] => [3] => ([],3)
=> ? ∊ {0,0,0,0,0,0,2,2,2,3}
[-,-,+] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,2,2,2,3}
[-,+,-] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,2,2,2,3}
[+,-,-] => [1,2,3] => [3] => ([],3)
=> ? ∊ {0,0,0,0,0,0,2,2,2,3}
[-,-,-] => [1,2,3] => [3] => ([],3)
=> ? ∊ {0,0,0,0,0,0,2,2,2,3}
[+,3,2] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[-,3,2] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,2,2,2,3}
[2,1,+] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[2,1,-] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,2,2,2,3}
[2,3,1] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,2,2,2,3}
[3,1,2] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[3,+,1] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[3,-,1] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? ∊ {0,0,0,0,0,0,2,2,2,3}
[+,+,+,+] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[+,-,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[+,+,-,+] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[+,+,+,-] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,+,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,-,+] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,+,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,-,+] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,+,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,+,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,+,4,3] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,+,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,-,4,3] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,-,4,3] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,3,2,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,3,2,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,3,2,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,3,2,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,3,4,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,3,4,2] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,4,2,3] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,4,2,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,4,+,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,4,+,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[+,4,-,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[-,4,-,2] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[2,1,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[2,1,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[2,1,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[2,1,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[2,1,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[2,3,1,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[2,3,1,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[2,3,4,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[2,4,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[2,4,+,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[2,4,-,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? ∊ {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4}
[3,1,2,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[3,+,1,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,1,2,3] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,1,+,2] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,+,1,3] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,+,+,1] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,+,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,-,+,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,-,+,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,+,-,+] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,+,5,4] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,4,3,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,5,3,4] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,5,+,3] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,3,2,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,4,2,3,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,5,2,3,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,5,2,+,3] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,5,+,2,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[2,1,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[3,1,2,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[3,+,1,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[4,1,2,3,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[4,1,+,2,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[4,+,1,3,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[4,+,+,1,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,1,2,3,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,1,2,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,1,+,2,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,1,+,+,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,+,1,3,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,+,1,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 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.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!