- FindStat

Identifier

Mp00185: Skew partitions —cell poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000456: Graphs ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 186 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

search for individual values

searching the database for the individual values of this statistic

Description

The monochromatic index of a connected graph.
This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path.
For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.

Map

cell poset

Description

The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.

Map

to graph

Description

Returns the Hasse diagram of the poset as an undirected graph.