Identifier
Values
[1] => [.,.] => [[]] => ([(0,1)],2) => 0
[1,2] => [.,[.,.]] => [[[]]] => ([(0,2),(2,1)],3) => 0
[2,1] => [[.,.],.] => [[],[]] => ([(0,2),(1,2)],3) => 0
[1,2,3] => [.,[.,[.,.]]] => [[[[]]]] => ([(0,3),(2,1),(3,2)],4) => 0
[1,3,2] => [.,[[.,.],.]] => [[[],[]]] => ([(0,3),(1,3),(3,2)],4) => 1
[2,1,3] => [[.,.],[.,.]] => [[],[[]]] => ([(0,3),(1,2),(2,3)],4) => 0
[2,3,1] => [[.,[.,.]],.] => [[[]],[]] => ([(0,3),(1,2),(2,3)],4) => 0
[3,1,2] => [[.,.],[.,.]] => [[],[[]]] => ([(0,3),(1,2),(2,3)],4) => 0
[3,2,1] => [[[.,.],.],.] => [[],[],[]] => ([(0,3),(1,3),(2,3)],4) => 1
[1,2,3,4] => [.,[.,[.,[.,.]]]] => [[[[[]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,2,4,3] => [.,[.,[[.,.],.]]] => [[[[],[]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => 1
[1,3,2,4] => [.,[[.,.],[.,.]]] => [[[],[[]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 1
[1,3,4,2] => [.,[[.,[.,.]],.]] => [[[[]],[]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 1
[1,4,2,3] => [.,[[.,.],[.,.]]] => [[[],[[]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 1
[1,4,3,2] => [.,[[[.,.],.],.]] => [[[],[],[]]] => ([(0,4),(1,4),(2,4),(4,3)],5) => 2
[2,1,3,4] => [[.,.],[.,[.,.]]] => [[],[[[]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
[2,1,4,3] => [[.,.],[[.,.],.]] => [[],[[],[]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => 1
[2,3,1,4] => [[.,[.,.]],[.,.]] => [[[]],[[]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 0
[2,3,4,1] => [[.,[.,[.,.]]],.] => [[[[]]],[]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
[2,4,1,3] => [[.,[.,.]],[.,.]] => [[[]],[[]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 0
[2,4,3,1] => [[.,[[.,.],.]],.] => [[[],[]],[]] => ([(0,4),(1,3),(2,3),(3,4)],5) => 1
[3,1,2,4] => [[.,.],[.,[.,.]]] => [[],[[[]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
[3,1,4,2] => [[.,.],[[.,.],.]] => [[],[[],[]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => 1
[3,2,1,4] => [[[.,.],.],[.,.]] => [[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[3,2,4,1] => [[[.,.],[.,.]],.] => [[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[3,4,1,2] => [[.,[.,.]],[.,.]] => [[[]],[[]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 0
[3,4,2,1] => [[[.,[.,.]],.],.] => [[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[4,1,2,3] => [[.,.],[.,[.,.]]] => [[],[[[]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 0
[4,1,3,2] => [[.,.],[[.,.],.]] => [[],[[],[]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => 1
[4,2,1,3] => [[[.,.],.],[.,.]] => [[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[4,2,3,1] => [[[.,.],[.,.]],.] => [[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[4,3,1,2] => [[[.,.],.],[.,.]] => [[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[4,3,2,1] => [[[[.,.],.],.],.] => [[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [[[[[[]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => [[[[[],[]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 1
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => [[[[],[[]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 1
[1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => [[[[[]],[]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 1
[1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => [[[[],[[]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 1
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => [[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 2
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => [[[],[[[]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 1
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 2
[1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => [[[[]],[[]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 1
[1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => [[[[[]]],[]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 1
[1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => [[[[]],[[]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 1
[1,3,5,4,2] => [.,[[.,[[.,.],.]],.]] => [[[[],[]],[]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 2
[1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => [[[],[[[]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 1
[1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 2
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => [[[],[],[[]]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 2
[1,4,3,5,2] => [.,[[[.,.],[.,.]],.]] => [[[],[[]],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 2
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => [[[[]],[[]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 1
[1,4,5,3,2] => [.,[[[.,[.,.]],.],.]] => [[[[]],[],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 2
[1,5,2,3,4] => [.,[[.,.],[.,[.,.]]]] => [[[],[[[]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 1
[1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 2
[1,5,3,2,4] => [.,[[[.,.],.],[.,.]]] => [[[],[],[[]]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 2
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => [[[],[[]],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 2
[1,5,4,2,3] => [.,[[[.,.],.],[.,.]]] => [[[],[],[[]]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 2
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => [[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 3
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 1
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[2,1,4,5,3] => [[.,.],[[.,[.,.]],.]] => [[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[2,1,5,3,4] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
[2,3,1,5,4] => [[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
[2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => [[[[[]]]],[]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
[2,3,5,1,4] => [[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
[2,3,5,4,1] => [[.,[.,[[.,.],.]]],.] => [[[[],[]]],[]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 1
[2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
[2,4,1,5,3] => [[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[2,4,3,1,5] => [[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[2,4,3,5,1] => [[.,[[.,.],[.,.]]],.] => [[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[2,4,5,1,3] => [[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
[2,4,5,3,1] => [[.,[[.,[.,.]],.]],.] => [[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
[2,5,1,4,3] => [[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[2,5,3,1,4] => [[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[2,5,3,4,1] => [[.,[[.,.],[.,.]]],.] => [[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[2,5,4,1,3] => [[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
[3,1,2,5,4] => [[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 1
[3,1,4,2,5] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[3,1,4,5,2] => [[.,.],[[.,[.,.]],.]] => [[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[3,1,5,2,4] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[3,2,4,1,5] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[3,2,4,5,1] => [[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[3,2,5,1,4] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[3,2,5,4,1] => [[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
[3,4,1,5,2] => [[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[3,4,2,1,5] => [[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[3,4,2,5,1] => [[[.,[.,.]],[.,.]],.] => [[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[3,4,5,1,2] => [[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
[3,4,5,2,1] => [[[.,[.,[.,.]]],.],.] => [[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[3,5,1,2,4] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
[3,5,1,4,2] => [[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[3,5,2,1,4] => [[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[3,5,2,4,1] => [[[.,[.,.]],[.,.]],.] => [[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[3,5,4,1,2] => [[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
>>> Load all 148 entries. <<<
[3,5,4,2,1] => [[[.,[[.,.],.]],.],.] => [[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
[4,1,2,5,3] => [[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 1
[4,1,3,2,5] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[4,1,3,5,2] => [[.,.],[[.,[.,.]],.]] => [[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[4,1,5,2,3] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[4,2,1,3,5] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[4,2,1,5,3] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[4,2,3,5,1] => [[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[4,2,5,1,3] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[4,2,5,3,1] => [[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[4,3,1,2,5] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[4,3,1,5,2] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[4,3,2,5,1] => [[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[4,3,5,1,2] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[4,3,5,2,1] => [[[[.,.],[.,.]],.],.] => [[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 0
[4,5,1,3,2] => [[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[4,5,2,1,3] => [[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[4,5,2,3,1] => [[[.,[.,.]],[.,.]],.] => [[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[4,5,3,2,1] => [[[[.,[.,.]],.],.],.] => [[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 0
[5,1,2,4,3] => [[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 1
[5,1,3,2,4] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[5,1,3,4,2] => [[.,.],[[.,[.,.]],.]] => [[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[5,1,4,2,3] => [[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[5,2,1,3,4] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[5,2,1,4,3] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[5,2,3,1,4] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[5,2,4,1,3] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => [[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[5,3,1,2,4] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[5,3,1,4,2] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[5,3,2,1,4] => [[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[5,3,4,1,2] => [[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[5,3,4,2,1] => [[[[.,.],[.,.]],.],.] => [[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[5,4,1,2,3] => [[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[5,4,1,3,2] => [[[.,.],.],[[.,.],.]] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[5,4,2,1,3] => [[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[5,4,2,3,1] => [[[[.,.],.],[.,.]],.] => [[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[5,4,3,1,2] => [[[[.,.],.],.],[.,.]] => [[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 3
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Description
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Map
to poset
Description
Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.
Map
to ordered tree: left child = left brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
  • if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
  • if $x$ is the right child of $y$, $x$ becomes the last child of $y$.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.