Identifier
Values
([],1) => [1] => -1
([],2) => [2] => 1
([(0,1)],2) => [1] => -1
([],3) => [3,3] => 2
([(1,2)],3) => [3] => 1
([(0,1),(0,2)],3) => [2] => 1
([(0,2),(2,1)],3) => [1] => -1
([(0,2),(1,2)],3) => [2] => 1
([(2,3)],4) => [4,4,4] => 3
([(1,2),(1,3)],4) => [8] => 1
([(0,1),(0,2),(0,3)],4) => [3,3] => 2
([(0,2),(0,3),(3,1)],4) => [3] => 1
([(0,1),(0,2),(1,3),(2,3)],4) => [2] => 1
([(1,2),(2,3)],4) => [4] => 1
([(0,3),(3,1),(3,2)],4) => [2] => 1
([(1,3),(2,3)],4) => [8] => 1
([(0,3),(1,3),(3,2)],4) => [2] => 1
([(0,3),(1,3),(2,3)],4) => [3,3] => 2
([(0,3),(1,2)],4) => [4,2] => 2
([(0,3),(1,2),(1,3)],4) => [3,2] => 2
([(0,2),(0,3),(1,2),(1,3)],4) => [2,2] => 2
([(0,3),(2,1),(3,2)],4) => [1] => -1
([(0,3),(1,2),(2,3)],4) => [3] => 1
([(0,2),(0,3),(0,4),(4,1)],5) => [4,4,4] => 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => [8] => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => [3,3] => 2
([(0,3),(0,4),(4,1),(4,2)],5) => [8] => 1
([(1,2),(1,3),(2,4),(3,4)],5) => [5,5] => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [2] => 1
([(0,3),(0,4),(3,2),(4,1)],5) => [4,2] => 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => [3,2] => 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => [2,2] => 2
([(1,4),(4,2),(4,3)],5) => [5,5] => 2
([(0,4),(4,1),(4,2),(4,3)],5) => [3,3] => 2
([(1,4),(2,4),(4,3)],5) => [5,5] => 2
([(0,4),(1,4),(4,2),(4,3)],5) => [2,2] => 2
([(0,4),(1,4),(2,4),(4,3)],5) => [3,3] => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [6,6] => 2
([(0,4),(1,4),(2,3),(4,2)],5) => [2] => 1
([(0,4),(1,3),(2,3),(3,4)],5) => [8] => 1
([(0,4),(1,4),(2,3),(3,4)],5) => [4,4,4] => 3
([(0,4),(1,2),(1,4),(2,3)],5) => [5,4] => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => [3,2] => 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => [6] => 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => [2,2] => 2
([(0,4),(1,2),(1,4),(4,3)],5) => [7] => 1
([(0,2),(0,4),(3,1),(4,3)],5) => [4] => 1
([(0,4),(1,2),(1,3),(3,4)],5) => [4,4,3] => 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => [3] => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [8] => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => [6,6] => 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => [5,3] => 2
([(0,3),(1,2),(1,4),(3,4)],5) => [5,4] => 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => [6] => 1
([(1,4),(3,2),(4,3)],5) => [5] => 1
([(0,3),(3,4),(4,1),(4,2)],5) => [2] => 1
([(0,4),(1,2),(2,4),(4,3)],5) => [3] => 1
([(0,3),(1,4),(4,2)],5) => [5,5] => 2
([(0,4),(3,2),(4,1),(4,3)],5) => [3] => 1
([(0,4),(1,2),(2,3),(2,4)],5) => [7] => 1
([(0,4),(2,3),(3,1),(4,2)],5) => [1] => -1
([(0,3),(1,2),(2,4),(3,4)],5) => [4,2] => 2
([(0,4),(1,2),(2,3),(3,4)],5) => [4] => 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [2] => 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => [3,3] => 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [6,6] => 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => [8] => 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => [5,5] => 2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => [2,2] => 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => [6] => 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [2,2] => 2
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => [7] => 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [6,6] => 2
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => [3,3] => 2
([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => [6,6] => 2
([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => [6,6] => 2
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => [3,3] => 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [6,6] => 2
([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => [8] => 1
([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => [6] => 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => [2,2] => 2
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => [5,5] => 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => [4,2] => 2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => [8] => 1
([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => [4,4,4] => 3
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [2] => 1
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [8] => 1
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [5,5] => 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [3,3] => 2
([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => [5,5] => 2
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [2,2] => 2
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => [6,2,2] => 3
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => [3,2] => 2
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => [4,4,2,2] => 4
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => [6,2,2] => 3
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => [2,2,2,2] => 4
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => [4,4] => 2
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => [2,2] => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => [6] => 1
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => [4,4,4] => 3
([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => [5,5] => 2
>>> Load all 307 entries. <<<
([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => [5,5] => 2
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => [5,4] => 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [3,2] => 2
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => [5,4] => 2
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => [5,3] => 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => [3] => 1
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => [8] => 1
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => [4,4,3] => 3
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => [4,4,3] => 3
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => [4] => 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [2] => 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => [5,5] => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => [6,6] => 2
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => [8,3] => 2
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => [5,3] => 2
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => [6] => 1
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => [7] => 1
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => [3,3,3] => 3
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [6] => 1
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => [5,4] => 2
([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => [5] => 1
([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => [8] => 1
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => [8,3] => 2
([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => [6] => 1
([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => [4,3,3] => 3
([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => [4,4,4] => 3
([(1,5),(3,4),(4,2),(5,3)],6) => [6] => 1
([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => [2] => 1
([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => 2
([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => [4] => 1
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => [4,4,2,2] => 4
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [2] => 1
([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => [4] => 1
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => [5,4] => 2
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => [7] => 1
([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => [5,4] => 2
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => [4,4] => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => [2,2] => 2
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => [3,2] => 2
([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => [4,2] => 2
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => [7] => 1
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => [3] => 1
([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => [5,4] => 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [1] => -1
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [3] => 1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [5] => 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [2] => 1
([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [5,5] => 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => [3] => 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7) => [6,6] => 2
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [6,6] => 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => [8] => 1
([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7) => [6,6] => 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => [2,2] => 2
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => [4,4,2,2] => 4
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => [6,2,2] => 3
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => [2,2,2,2] => 4
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [6,6] => 2
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => [6] => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7) => [6,6] => 2
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => [3,3] => 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => [3,3] => 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => [6,6] => 2
([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => [6,6] => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => [6,6] => 2
([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7) => [6,6] => 2
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => [6] => 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => [5,5] => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => [7] => 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => [2,2] => 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => [2,2] => 2
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => [4,4] => 2
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => [2,2] => 2
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [5] => 1
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [2] => 1
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => [2] => 1
([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => [8] => 1
([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => [5,5] => 2
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => [2,2] => 2
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => [4,4,2,2] => 4
([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => [8] => 1
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => [6,2,2] => 3
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => [2,2,2,2] => 4
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => [4,4,2,2] => 4
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => [6,2,2] => 3
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => [2,2,2,2] => 4
([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => [4,4,4] => 3
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => [6] => 1
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => [6] => 1
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => [6,2,2] => 3
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => [5,4] => 2
([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => [6,6] => 2
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => [2,2,2,2] => 4
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => [6,6] => 2
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => [4,4,2,2] => 4
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => [10] => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => [2,2] => 2
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => [6] => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => [4,4] => 2
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => [6,6] => 2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => [4,4,4] => 3
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => [5,5] => 2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => [3,3] => 2
([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7) => [6,2,2] => 3
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [3,2] => 2
([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7) => [4,3,3] => 3
([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7) => [8,3] => 2
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7) => [5,3] => 2
([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7) => [5,4] => 2
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => [4] => 1
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7) => [4,4] => 2
([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7) => [5,4] => 2
([(0,5),(1,3),(1,4),(3,6),(4,5),(5,6),(6,2)],7) => [4,4,3] => 3
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7) => [8] => 1
([(0,5),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => [5,5] => 2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [2] => 1
([(0,6),(1,3),(1,4),(3,5),(4,5),(5,6),(6,2)],7) => [5,5] => 2
([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7) => [6] => 1
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7) => [4,4] => 2
([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7) => [6] => 1
([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7) => [5,4] => 2
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => [4,2] => 2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7) => [6,6] => 2
([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) => [11,7,3] => 3
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) => [3,3,3] => 3
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7) => [6] => 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => [7] => 1
([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7) => [8,3] => 2
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7) => [2,2] => 2
([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) => [6,3,3,3] => 4
([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => [6,6] => 2
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => [5,4] => 2
([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7) => [8,3] => 2
([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7) => [7] => 1
([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7) => [5,4] => 2
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [3,2] => 2
([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => [4,4] => 2
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7) => [6] => 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7) => [2,2] => 2
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7) => [2,2] => 2
([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) => [7] => 1
([(0,5),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => [5,5] => 2
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => [3,3] => 2
([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7) => [5,5] => 2
([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7) => [3,3] => 2
([(0,5),(1,4),(4,6),(5,6),(6,2),(6,3)],7) => [4,4,2,2] => 4
([(0,3),(1,2),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [4,4,2,2] => 4
([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7) => [5,5] => 2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => [3] => 1
([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [5,5] => 2
([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7) => [4,4] => 2
([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) => [7] => 1
([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) => [6,3,3,3] => 4
([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => [6,2,2] => 3
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) => [3,2] => 2
([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) => [5,4] => 2
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => [5,4] => 2
([(0,5),(2,6),(3,6),(4,1),(4,3),(5,2),(5,4)],7) => [4,4,3] => 3
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => [5] => 1
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => [5,5] => 2
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => [3] => 1
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => [4,4,3] => 3
([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7) => [8] => 1
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => [8] => 1
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7) => [6,6] => 2
([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7) => [5,3] => 2
([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) => [9,5] => 2
([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) => [5,3] => 2
([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7) => [8,3] => 2
([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7) => [6] => 1
([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) => [3,3,3] => 3
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7) => [6] => 1
([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7) => [10] => 1
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7) => [2,2] => 2
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) => [3,2] => 2
([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) => [9,5] => 2
([(0,5),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4)],7) => [5,4] => 2
([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => [6] => 1
([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7) => [8] => 1
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => [5,5] => 2
([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7) => [6] => 1
([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7) => [4,4,4] => 3
([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => [7] => 1
([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) => [2] => 1
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) => [4] => 1
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7) => [5] => 1
([(0,5),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3)],7) => [7] => 1
([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7) => [3,3,3] => 3
([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) => [4,3,3] => 3
([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7) => [4,2] => 2
([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) => [5,4] => 2
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => [3] => 1
([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7) => [5,5] => 2
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [1] => -1
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [3] => 1
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => [4,4,4] => 3
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => [3] => 1
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => [4,2] => 2
([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => [4,2] => 2
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7) => [8] => 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [2] => 1
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => [4] => 1
([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => [6] => 1
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [2] => 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => [4] => 1
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [3,2] => 2
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Description
The Andrews-Garvan crank of a partition.
If $\pi$ is a partition, let $l(\pi)$ be its length (number of parts), $\omega(\pi)$ be the number of parts equal to 1, and $\mu(\pi)$ be the number of parts larger than $\omega(\pi)$. The crank is then defined by
$$ c(\pi) = \begin{cases} l(\pi) &\text{if \(\omega(\pi)=0\)}\\ \mu(\pi) - \omega(\pi) &\text{otherwise}. \end{cases} $$
This statistic was defined in [1] to explain Ramanujan's partition congruence $$p(11n+6) \equiv 0 \pmod{11}$$ in the same way as the Dyson rank (St000145The Dyson rank of a partition.) explains the congruences $$p(5n+4) \equiv 0 \pmod{5}$$ and $$p(7n+5) \equiv 0 \pmod{7}.$$
Map
promotion cycle type
Description
The cycle type of promotion on the linear extensions of a poset.