Identifier
Values
([],1) => [1] => [1,0,1,0] => [1,1,0,0] => 1
([],2) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,1)],2) => [1] => [1,0,1,0] => [1,1,0,0] => 1
([],3) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(1,2)],3) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,1),(0,2)],3) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,2),(2,1)],3) => [1] => [1,0,1,0] => [1,1,0,0] => 1
([(0,2),(1,2)],3) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,1),(0,2),(0,3)],4) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,2),(0,3),(3,1)],4) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,1),(0,2),(1,3),(2,3)],4) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(1,2),(2,3)],4) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 3
([(0,3),(3,1),(3,2)],4) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,3),(1,3),(3,2)],4) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,3),(1,3),(2,3)],4) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,3),(1,2)],4) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 3
([(0,3),(1,2),(1,3)],4) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,2),(0,3),(1,2),(1,3)],4) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,3),(2,1),(3,2)],4) => [1] => [1,0,1,0] => [1,1,0,0] => 1
([(0,3),(1,2),(2,3)],4) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,3),(0,4),(3,2),(4,1)],5) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 3
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,4),(4,1),(4,2),(4,3)],5) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,4),(1,4),(4,2),(4,3)],5) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,4),(1,4),(2,4),(4,3)],5) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,4),(1,4),(2,3),(4,2)],5) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,4),(1,2),(1,4),(2,3)],5) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,2),(0,4),(3,1),(4,3)],5) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 3
([(0,4),(1,2),(1,3),(3,4)],5) => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
([(0,3),(1,2),(1,4),(3,4)],5) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(1,4),(3,2),(4,3)],5) => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 3
([(0,3),(3,4),(4,1),(4,2)],5) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,4),(1,2),(2,4),(4,3)],5) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,4),(3,2),(4,1),(4,3)],5) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,4),(2,3),(3,1),(4,2)],5) => [1] => [1,0,1,0] => [1,1,0,0] => 1
([(0,3),(1,2),(2,4),(3,4)],5) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 3
([(0,4),(1,2),(2,3),(3,4)],5) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 3
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 3
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 3
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 4
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 3
([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 3
([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 3
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 3
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 3
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [1] => [1,0,1,0] => [1,1,0,0] => 1
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 3
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
([(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] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
>>> Load all 173 entries. <<<
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 3
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
([(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] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 3
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7) => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7) => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 3
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,5),(1,3),(1,4),(3,6),(4,5),(5,6),(6,2)],7) => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 3
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 4
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7) => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
([(0,5),(1,4),(4,6),(5,6),(6,2),(6,3)],7) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
([(0,3),(1,2),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7) => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,5),(2,6),(3,6),(4,1),(4,3),(5,2),(5,4)],7) => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 3
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => [4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 3
([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7) => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 3
([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 4
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7) => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 1
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
([(0,5),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 3
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7) => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 3
([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7) => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 4
([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 3
([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [1] => [1,0,1,0] => [1,1,0,0] => 1
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => [3] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => 2
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 3
([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 3
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 3
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [2] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 3
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => [3,2] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
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 degree of the standard monomial associated to a Dyck path relative to the diagonal boundary.
Given two lattice paths $U,L$ from $(0,0)$ to $(d,n-d)$, [1] describes a bijection between lattice paths weakly between $U$ and $L$ and subsets of $\{1,\dots,n\}$ such that the set of all such subsets gives the standard complex of the lattice path matroid $M[U,L]$.
This statistic gives the cardinality of the image of this bijection when a Dyck path is considered as a path weakly above the diagonal and relative to the diagonal boundary.
Map
promotion cycle type
Description
The cycle type of promotion on the linear extensions of a poset.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.