- FindStat

Identifier

Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001330: Graphs ⟶ ℤ

Values

[[1,2]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[2,2]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[1],[2]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[1,3]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[2,3]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[3,3]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[1],[3]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[2],[3]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[1,1,2]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,2,2]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,2,2]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,4]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[2,4]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[3,4]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[4,4]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[1],[4]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[2],[4]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[3],[4]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[1,1,3]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,2,3]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,3,3]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,2,3]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,3,3]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,3,3]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1],[2],[3]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1,1,1,2]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,2,2]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,2,2]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,2,2]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,5]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[2,5]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[3,5]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[4,5]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[5,5]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[1],[5]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[2],[5]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[3],[5]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[4],[5]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[1,1,4]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,2,4]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,3,4]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,4,4]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,2,4]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,3,4]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,4,4]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,3,4]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,4,4]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[4,4,4]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1],[2],[4]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1],[3],[4]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[2],[3],[4]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1,1,1,3]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,2,3]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,3,3]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,2,3]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,3,3]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,3,3,3]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,2,3]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,3,3]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,3,3,3]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,3,3,3]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,1,1,2]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,1,2,2]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,2,2,2]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,2,2,2]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,2,2,2]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,6]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[2,6]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[3,6]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[4,6]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[5,6]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[6,6]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[1],[6]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[2],[6]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[3],[6]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[4],[6]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[5],[6]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[1,1,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,2,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,3,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,4,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,5,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,2,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,3,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,4,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,5,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,3,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,4,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,5,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[4,4,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[4,5,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[5,5,5]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1],[2],[5]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1],[3],[5]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1],[4],[5]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[2],[3],[5]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[2],[4],[5]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[3],[4],[5]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1,1,1,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,2,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,3,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

>>> Load all 578 entries. <<<

[[1,1,4,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,2,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,3,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,4,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,3,3,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,3,4,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,4,4,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,2,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,3,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,4,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,3,3,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,3,4,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,4,4,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,3,3,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,3,4,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,4,4,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[4,4,4,4]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1],[2],[3],[4]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[1,1,1,1,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,1,2,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,1,3,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,2,2,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,2,3,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,3,3,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,2,2,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,2,3,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,3,3,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,3,3,3,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,2,2,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,2,3,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,3,3,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,3,3,3,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,3,3,3,3]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,1,1,1,2]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,1,2,2]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,2,2,2]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,2,2,2,2]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,2,2,2,2]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,2,2,2,2]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,7]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[2,7]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[3,7]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[4,7]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[5,7]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[6,7]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[7,7]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[1],[7]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[2],[7]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[3],[7]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[4],[7]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[5],[7]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[6],[7]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[1,1,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,2,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,3,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,4,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,5,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,6,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,2,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,3,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,4,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,5,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,6,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,3,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,4,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,5,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,6,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[4,4,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[4,5,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[4,6,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[5,5,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[5,6,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[6,6,6]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1],[2],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1],[3],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1],[4],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1],[5],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[2],[3],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[2],[4],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[2],[5],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[3],[4],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[3],[5],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[4],[5],[6]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1,1,1,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,2,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,3,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,4,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,2,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,3,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,4,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,3,3,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,3,4,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,3,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,4,4,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,4,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,5,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,2,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,3,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,4,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,3,3,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,3,4,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,3,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,4,4,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,4,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,5,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,3,3,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,3,4,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,3,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,4,4,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,4,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,5,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[4,4,4,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[4,4,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[4,5,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[5,5,5,5]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1],[2],[3],[5]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[1],[2],[4],[5]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[1],[3],[4],[5]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[2],[3],[4],[5]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[1,1,1,1,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,1,2,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,1,3,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,1,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,2,2,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,2,3,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,2,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,3,3,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,3,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,4,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,2,2,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,2,3,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,2,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,3,3,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,3,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,4,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,3,3,3,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,3,3,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,3,4,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,4,4,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,2,2,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,2,3,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,2,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,3,3,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,3,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,4,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,3,3,3,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,3,3,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,3,4,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,4,4,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,3,3,3,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,3,3,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,3,4,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,4,4,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[4,4,4,4,4]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,1,1,1,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,1,2,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,1,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,2,2,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,2,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,2,2,2,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,2,2,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,2,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,3,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,2,2,2,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,2,2,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,2,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,3,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,3,3,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,2,2,2,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,2,2,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,2,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,3,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,3,3,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[3,3,3,3,3,3]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,1,1,1,2]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,1,1,1,2,2]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,1,1,2,2,2]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,1,2,2,2,2]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,2,2,2,2,2]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,8]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[2,8]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[3,8]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[4,8]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[5,8]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[6,8]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[7,8]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[8,8]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[1],[8]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[2],[8]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[3],[8]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[4],[8]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[5],[8]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[6],[8]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[7],[8]] => [2,1] => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 3

[[1,1,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,2,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,3,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,4,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,5,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,6,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1,7,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,2,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,3,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,4,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,5,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,6,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[2,7,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,3,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,4,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,5,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,6,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[3,7,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[4,4,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[4,5,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[4,6,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[4,7,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[5,5,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[5,6,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[5,7,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[6,6,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[6,7,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[7,7,7]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[1],[2],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1],[3],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1],[4],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1],[5],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1],[6],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[2],[3],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[2],[4],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[2],[5],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[2],[6],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[3],[4],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[3],[5],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[3],[6],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[4],[5],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[4],[6],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[5],[6],[7]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4

[[1,1,1,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,2,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,3,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,4,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,1,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,2,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,3,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,4,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,2,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,3,3,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,3,4,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,3,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,3,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,4,4,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,4,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,4,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,5,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,5,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1,6,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,2,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,3,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,4,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,2,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,3,3,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,3,4,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,3,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,3,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,4,4,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,4,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,4,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,5,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,5,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[2,6,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,3,3,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,3,4,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,3,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,3,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,4,4,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,4,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,4,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,5,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,5,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[3,6,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[4,4,4,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[4,4,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[4,4,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[4,5,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[4,5,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[4,6,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[5,5,5,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[5,5,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[5,6,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[6,6,6,6]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[1],[2],[3],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[1],[2],[4],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[1],[2],[5],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[1],[3],[4],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[1],[3],[5],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[1],[4],[5],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[2],[3],[4],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[2],[3],[5],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[2],[4],[5],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[3],[4],[5],[6]] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5

[[1,1,1,1,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,1,2,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,1,3,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,1,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,1,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,2,2,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,2,3,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,2,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,2,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,3,3,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,3,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,3,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,4,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,4,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,1,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,2,2,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,2,3,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,2,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,2,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,3,3,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,3,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,3,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,4,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,4,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,2,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,3,3,3,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,3,3,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,3,3,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,3,4,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,3,4,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,3,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,4,4,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,4,4,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,4,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1,5,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,2,2,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,2,3,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,2,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,2,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,3,3,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,3,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,3,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,4,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,4,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,2,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,3,3,3,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,3,3,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,3,3,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,3,4,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,3,4,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,3,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,4,4,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,4,4,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,4,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[2,5,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,3,3,3,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,3,3,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,3,3,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,3,4,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,3,4,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,3,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,4,4,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,4,4,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,4,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[3,5,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[4,4,4,4,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[4,4,4,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[4,4,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[4,5,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[5,5,5,5,5]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6

[[1,1,1,1,1,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,1,2,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,1,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,1,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,2,2,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,2,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,2,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,2,2,2,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,2,2,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,2,2,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,2,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,2,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,2,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,3,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,3,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,3,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,2,2,2,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,2,2,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,2,2,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,2,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,2,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,2,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,3,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,3,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,3,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,3,3,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,3,3,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,3,3,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,3,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,4,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,2,2,2,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,2,2,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,2,2,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,2,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,2,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,2,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,3,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,3,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,3,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,2,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,3,3,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,3,3,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,3,3,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,3,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[2,4,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[3,3,3,3,3,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[3,3,3,3,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[3,3,3,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[3,3,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[3,4,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[4,4,4,4,4,4]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,1,1,1,1,1,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,1,1,1,2,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,1,1,1,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,1,1,2,2,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,1,1,2,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,1,1,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,1,2,2,2,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,1,2,2,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,1,2,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,1,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,2,2,2,2,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,2,2,2,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,2,2,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,2,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,1,3,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,2,2,2,2,2,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,2,2,2,2,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,2,2,2,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,2,2,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,2,3,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[2,2,2,2,2,2,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[2,2,2,2,2,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[2,2,2,2,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[2,2,2,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[2,2,3,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[2,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[3,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => ([],7) => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2

[[1]] => [1] => ([],1) => ([(0,1)],2) => 2

[[2]] => [1] => ([],1) => ([(0,1)],2) => 2

[[1,1]] => [1,2] => ([],2) => ([(0,2),(1,2)],3) => 2

[[3]] => [1] => ([],1) => ([(0,1)],2) => 2

[[1,1,1]] => [1,2,3] => ([],3) => ([(0,3),(1,3),(2,3)],4) => 2

[[4]] => [1] => ([],1) => ([(0,1)],2) => 2

[[1,1,1,1]] => [1,2,3,4] => ([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

[[5]] => [1] => ([],1) => ([(0,1)],2) => 2

[[1,1,1,1,1]] => [1,2,3,4,5] => ([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

[[6]] => [1] => ([],1) => ([(0,1)],2) => 2

[[1,1,1,1,1,1]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => ([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7

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Description

The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.

Map

cone

Description

The cone of a graph.
The cone of a graph is obtained by joining a new vertex to all the vertices of the graph. The added vertex is called a universal vertex or a dominating vertex.

Map

reading word permutation

Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).

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.