Identifier
Values
[+] => [1] => ([],1) => 0
[-] => [1] => ([],1) => 0
[-,+] => [2,1] => ([(0,1)],2) => 1
[-,+,+] => [2,3,1] => ([(0,2),(1,2)],3) => 2
[-,-,+] => [3,1,2] => ([(0,2),(1,2)],3) => 2
[-,+,+,+] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => 2
[-,-,+,+] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[-,+,-,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => 3
[-,-,-,+] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => 2
[-,3,2,+] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => 3
[4,-,+,1] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4) => 3
[-,+,+,+,+] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[-,-,+,+,+] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2
[-,+,-,+,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 3
[-,+,+,-,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[-,-,-,+,+] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2
[-,-,+,-,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 3
[-,+,-,-,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[-,-,-,-,+] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[-,+,4,3,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[-,-,4,3,+] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 3
[-,3,2,+,+] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 3
[-,3,2,-,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[-,3,4,2,+] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[-,4,2,3,+] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[-,4,+,2,+] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 3
[-,4,-,2,+] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 3
[-,5,-,2,4] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 4
[-,5,-,+,2] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 3
[2,4,+,1,+] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5) => 4
[2,5,-,+,1] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[4,-,+,1,+] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 3
[5,-,+,1,4] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[5,-,+,+,1] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 3
[5,+,-,+,1] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 4
[5,-,-,+,1] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 3
[5,-,+,-,1] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5) => 4
[5,-,4,3,1] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5) => 4
[5,3,2,+,1] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 4
[-,+,+,+,+,+] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[-,-,+,+,+,+] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
[-,+,-,+,+,+] => [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3
[-,+,+,-,+,+] => [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,+,+,+,-,+] => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
[-,-,-,+,+,+] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2
[-,-,+,-,+,+] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 3
[-,-,+,+,-,+] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,+,-,-,+,+] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,+,-,+,-,+] => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,+,+,-,-,+] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 3
[-,-,-,-,+,+] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
[-,-,-,+,-,+] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3
[-,-,+,-,-,+] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,+,-,-,-,+] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
[-,-,-,-,-,+] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[-,+,+,5,4,+] => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
[-,-,+,5,4,+] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,+,-,5,4,+] => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,-,-,5,4,+] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3
[-,+,4,3,+,+] => [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,-,4,3,+,+] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 3
[-,+,4,3,-,+] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 3
[-,-,4,3,-,+] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,+,4,5,3,+] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 3
[-,-,4,5,3,+] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,+,5,3,4,+] => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
[-,-,5,3,4,+] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,+,5,+,3,+] => [2,4,3,6,1,5] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[-,-,5,+,3,+] => [4,3,6,1,2,5] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,+,5,-,3,+] => [2,3,6,1,5,4] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 3
[-,-,5,-,3,+] => [3,6,1,2,5,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 3
[-,+,6,-,3,5] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[-,-,6,-,3,5] => [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[-,+,6,-,+,3] => [2,5,3,1,6,4] => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 4
[-,-,6,-,+,3] => [5,3,1,2,6,4] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 3
[-,3,2,+,+,+] => [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3
[-,3,2,-,+,+] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,3,2,+,-,+] => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,3,2,-,-,+] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
[-,3,2,5,4,+] => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,3,4,2,+,+] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,3,4,2,-,+] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
[-,3,4,5,2,+] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
[-,3,5,2,4,+] => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,3,5,+,2,+] => [4,2,6,1,3,5] => ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 3
[-,3,5,-,2,+] => [2,6,1,3,5,4] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[-,3,6,-,2,5] => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 4
[-,3,6,-,+,2] => [5,2,1,3,6,4] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[-,4,2,3,+,+] => [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,4,2,3,-,+] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 3
[-,4,2,5,3,+] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 3
[-,4,+,2,+,+] => [3,2,5,6,1,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 3
[-,4,-,2,+,+] => [2,5,6,1,4,3] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,4,+,2,-,+] => [3,2,6,1,4,5] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 3
[-,4,-,2,-,+] => [2,6,1,4,3,5] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[-,4,+,5,2,+] => [3,2,6,1,4,5] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 3
[-,4,-,5,2,+] => [2,6,1,4,3,5] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[-,4,5,2,3,+] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 3
[-,4,5,3,2,+] => [3,2,6,1,4,5] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 3
[-,5,2,3,4,+] => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
[-,5,2,+,3,+] => [2,4,3,6,1,5] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
>>> Load all 219 entries. <<<
[-,5,2,-,3,+] => [2,3,6,1,5,4] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 3
[-,5,+,2,4,+] => [3,2,4,6,1,5] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[-,5,-,2,4,+] => [2,4,6,1,5,3] => ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 3
[-,5,+,+,2,+] => [3,4,2,6,1,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 3
[-,5,-,+,2,+] => [4,2,6,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 3
[-,5,+,-,2,+] => [3,2,6,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 3
[-,5,-,-,2,+] => [2,6,1,5,3,4] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 3
[-,5,4,2,3,+] => [2,3,6,1,5,4] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 3
[-,5,4,3,2,+] => [3,2,6,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 3
[-,6,2,-,3,5] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[-,6,2,-,+,3] => [2,5,3,1,6,4] => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 4
[-,6,-,2,4,5] => [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[-,6,-,2,+,4] => [2,5,4,1,6,3] => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 4
[-,6,-,2,-,4] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[-,6,-,+,2,5] => [4,2,5,1,6,3] => ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 3
[-,6,+,-,2,5] => [3,2,5,1,6,4] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[-,6,-,-,2,5] => [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[-,6,-,+,+,2] => [4,5,2,1,6,3] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[-,6,+,-,+,2] => [3,5,2,1,6,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 4
[-,6,-,-,+,2] => [5,2,1,6,3,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 3
[-,6,-,+,-,2] => [4,2,1,6,3,5] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[-,6,-,5,2,4] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[-,6,-,5,4,2] => [4,2,1,6,3,5] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[-,6,4,2,3,5] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[-,6,4,2,+,3] => [2,5,3,1,6,4] => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 4
[-,6,4,3,2,5] => [3,2,5,1,6,4] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[-,6,4,3,+,2] => [3,5,2,1,6,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 4
[2,3,5,+,1,+] => [4,1,6,2,3,5] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[2,3,6,-,+,1] => [5,1,2,3,6,4] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
[2,4,+,1,+,+] => [3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[2,4,+,1,-,+] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[2,4,+,5,1,+] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[2,4,5,3,1,+] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[2,5,+,1,4,+] => [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 4
[2,5,+,+,1,+] => [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[2,5,-,+,1,+] => [4,1,6,2,5,3] => ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 3
[2,5,+,-,1,+] => [3,1,6,2,5,4] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[2,5,4,3,1,+] => [3,1,6,2,5,4] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[2,6,-,+,1,5] => [4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[2,6,+,-,1,5] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[2,6,-,+,+,1] => [4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[2,6,+,-,+,1] => [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[2,6,-,-,+,1] => [5,1,2,6,3,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 3
[2,6,-,+,-,1] => [4,1,2,6,3,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[2,6,-,5,4,1] => [4,1,2,6,3,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[2,6,4,3,1,5] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[2,6,4,3,+,1] => [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[3,+,5,+,1,+] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[3,-,5,+,1,+] => [4,1,6,3,2,5] => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 4
[3,+,6,-,+,1] => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 4
[3,-,6,-,+,1] => [5,1,3,2,6,4] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[3,5,2,+,1,+] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[3,6,2,-,+,1] => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 4
[3,6,4,2,+,1] => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 4
[4,-,+,1,+,+] => [3,1,5,6,4,2] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 3
[4,-,+,1,-,+] => [3,1,6,4,2,5] => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,-,+,5,1,+] => [3,1,6,4,2,5] => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,-,5,3,1,+] => [3,1,6,4,2,5] => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 4
[4,6,-,2,+,1] => [2,5,1,4,6,3] => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 4
[5,-,+,1,4,+] => [3,1,4,6,5,2] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[5,-,+,+,1,+] => [3,4,1,6,5,2] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 3
[5,+,-,+,1,+] => [2,4,1,6,5,3] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[5,-,-,+,1,+] => [4,1,6,5,2,3] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[5,-,+,-,1,+] => [3,1,6,5,2,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 4
[5,-,4,3,1,+] => [3,1,6,5,2,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 4
[5,-,6,-,3,1] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[5,3,2,+,1,+] => [2,4,1,6,5,3] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[5,6,-,2,4,1] => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[5,6,-,+,1,2] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 3
[5,6,-,+,2,1] => [4,2,1,5,6,3] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 3
[6,-,+,1,4,5] => [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 3
[6,-,+,1,+,4] => [3,1,5,4,6,2] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[6,-,+,1,-,4] => [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 4
[6,-,+,+,1,5] => [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 3
[6,+,-,+,1,5] => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[6,-,-,+,1,5] => [4,1,5,6,2,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[6,-,+,-,1,5] => [3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[6,-,+,+,+,1] => [3,4,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3
[6,+,-,+,+,1] => [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[6,+,+,-,+,1] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[6,-,-,+,+,1] => [4,5,1,6,2,3] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 3
[6,-,+,-,+,1] => [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 3
[6,-,+,+,-,1] => [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[6,+,-,-,+,1] => [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[6,+,-,+,-,1] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[6,-,-,-,+,1] => [5,1,6,2,3,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3
[6,-,-,+,-,1] => [4,1,6,2,3,5] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[6,-,+,-,-,1] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[6,-,+,5,1,4] => [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 4
[6,-,+,5,4,1] => [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[6,+,-,5,4,1] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[6,-,-,5,4,1] => [4,1,6,2,3,5] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[6,-,4,3,1,5] => [3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[6,+,4,3,+,1] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[6,-,4,3,+,1] => [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 3
[6,-,4,3,-,1] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[6,-,4,5,3,1] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[6,-,5,3,1,4] => [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 4
[6,-,5,3,4,1] => [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[6,-,5,+,1,3] => [4,1,3,6,2,5] => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 4
[6,-,5,+,3,1] => [4,3,1,6,2,5] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 4
[6,-,5,-,3,1] => [3,1,6,2,5,4] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[6,3,2,+,1,5] => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[6,3,2,+,+,1] => [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[6,3,2,-,+,1] => [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[6,3,2,+,-,1] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[6,3,2,5,4,1] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[6,3,4,2,+,1] => [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[6,3,5,2,4,1] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[6,3,5,+,1,2] => [4,1,2,6,3,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[6,3,5,+,2,1] => [4,2,1,6,3,5] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[6,4,2,3,+,1] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
[6,4,+,1,+,2] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[6,4,+,2,+,1] => [3,2,5,1,6,4] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[6,4,-,2,+,1] => [2,5,1,6,4,3] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 4
[6,5,-,2,4,1] => [2,4,1,6,5,3] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[6,5,-,+,1,2] => [4,1,2,6,5,3] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 3
[6,5,-,+,2,1] => [4,2,1,6,5,3] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 3
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Map
lower permutation
Description
The lower bound in the Grassmann interval corresponding to the decorated permutation.
Let $I$ be the anti-exceedance set of a decorated permutation $w$. Let $v$ be the $k$-Grassmannian permutation determined by $v[k] = w^{-1}(I)$ and let $u$ be the permutation satisfying $u = wv$. Then $[u, v]$ is the Grassmann interval corresponding to $w$.
This map returns $u$.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.