Identifier
Mp00180:
Integer compositions
—to ribbon⟶
Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00185: Skew partitions —cell poset⟶ Posets
Images
=>
Cc0028;cc-rep-1Cc0014;cc-rep-2
[1]=>[[1],[]]=>([],1)
[1,1]=>[[1,1],[]]=>([(0,1)],2)
[2]=>[[2],[]]=>([(0,1)],2)
[1,1,1]=>[[1,1,1],[]]=>([(0,2),(2,1)],3)
[1,2]=>[[2,1],[]]=>([(0,1),(0,2)],3)
[2,1]=>[[2,2],[1]]=>([(0,2),(1,2)],3)
[3]=>[[3],[]]=>([(0,2),(2,1)],3)
[1,1,1,1]=>[[1,1,1,1],[]]=>([(0,3),(2,1),(3,2)],4)
[1,1,2]=>[[2,1,1],[]]=>([(0,2),(0,3),(3,1)],4)
[1,2,1]=>[[2,2,1],[1]]=>([(0,3),(1,2),(1,3)],4)
[1,3]=>[[3,1],[]]=>([(0,2),(0,3),(3,1)],4)
[2,1,1]=>[[2,2,2],[1,1]]=>([(0,3),(1,2),(2,3)],4)
[2,2]=>[[3,2],[1]]=>([(0,3),(1,2),(1,3)],4)
[3,1]=>[[3,3],[2]]=>([(0,3),(1,2),(2,3)],4)
[4]=>[[4],[]]=>([(0,3),(2,1),(3,2)],4)
[1,1,1,1,1]=>[[1,1,1,1,1],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)
[1,1,1,2]=>[[2,1,1,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)
[1,1,2,1]=>[[2,2,1,1],[1]]=>([(0,4),(1,2),(1,4),(2,3)],5)
[1,1,3]=>[[3,1,1],[]]=>([(0,3),(0,4),(3,2),(4,1)],5)
[1,2,1,1]=>[[2,2,2,1],[1,1]]=>([(0,3),(1,2),(1,4),(3,4)],5)
[1,2,2]=>[[3,2,1],[1]]=>([(0,3),(0,4),(1,2),(1,4)],5)
[1,3,1]=>[[3,3,1],[2]]=>([(0,4),(1,2),(1,3),(3,4)],5)
[1,4]=>[[4,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)
[2,1,1,1]=>[[2,2,2,2],[1,1,1]]=>([(0,4),(1,2),(2,3),(3,4)],5)
[2,1,2]=>[[3,2,2],[1,1]]=>([(0,4),(1,2),(1,3),(3,4)],5)
[2,2,1]=>[[3,3,2],[2,1]]=>([(0,4),(1,3),(2,3),(2,4)],5)
[2,3]=>[[4,2],[1]]=>([(0,4),(1,2),(1,4),(2,3)],5)
[3,1,1]=>[[3,3,3],[2,2]]=>([(0,3),(1,2),(2,4),(3,4)],5)
[3,2]=>[[4,3],[2]]=>([(0,3),(1,2),(1,4),(3,4)],5)
[4,1]=>[[4,4],[3]]=>([(0,4),(1,2),(2,3),(3,4)],5)
[5]=>[[5],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)
[1,1,1,1,1,1]=>[[1,1,1,1,1,1],[]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,1,1,2]=>[[2,1,1,1,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
[1,1,1,3]=>[[3,1,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
[1,1,2,2]=>[[3,2,1,1],[1]]=>([(0,3),(0,5),(1,4),(1,5),(4,2)],6)
[1,1,3,1]=>[[3,3,1,1],[2]]=>([(0,5),(1,3),(1,4),(3,5),(4,2)],6)
[1,1,4]=>[[4,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
[1,2,1,2]=>[[3,2,2,1],[1,1]]=>([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
[1,2,2,1]=>[[3,3,2,1],[2,1]]=>([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
[1,2,3]=>[[4,2,1],[1]]=>([(0,3),(0,5),(1,4),(1,5),(4,2)],6)
[1,3,1,1]=>[[3,3,3,1],[2,2]]=>([(0,4),(1,2),(1,3),(3,5),(4,5)],6)
[1,3,2]=>[[4,3,1],[2]]=>([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
[1,4,1]=>[[4,4,1],[3]]=>([(0,5),(1,2),(1,4),(3,5),(4,3)],6)
[1,5]=>[[5,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
[2,1,1,1,1]=>[[2,2,2,2,2],[1,1,1,1]]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>([(0,5),(1,2),(1,4),(3,5),(4,3)],6)
[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[2,1,3]=>[[4,2,2],[1,1]]=>([(0,5),(1,3),(1,4),(3,5),(4,2)],6)
[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
[2,2,2]=>[[4,3,2],[2,1]]=>([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
[2,3,1]=>[[4,4,2],[3,1]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[2,4]=>[[5,2],[1]]=>([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[3,1,2]=>[[4,3,3],[2,2]]=>([(0,4),(1,2),(1,3),(3,5),(4,5)],6)
[3,2,1]=>[[4,4,3],[3,2]]=>([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
[3,3]=>[[5,3],[2]]=>([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
[4,1,1]=>[[4,4,4],[3,3]]=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[4,2]=>[[5,4],[3]]=>([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
[5,1]=>[[5,5],[4]]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[6]=>[[6],[]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1],[]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,1,1,2]=>[[2,1,1,1,1,1],[]]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
[1,1,1,1,3]=>[[3,1,1,1,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7)
[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>([(0,5),(0,6),(1,3),(1,6),(4,2),(5,4)],7)
[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>([(0,6),(1,3),(1,5),(3,6),(4,2),(5,4)],7)
[1,1,1,4]=>[[4,1,1,1],[]]=>([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>([(0,5),(0,6),(1,3),(1,4),(4,6),(5,2)],7)
[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4)],7)
[1,1,2,3]=>[[4,2,1,1],[1]]=>([(0,5),(0,6),(1,4),(1,6),(4,2),(5,3)],7)
[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>([(0,4),(1,3),(1,5),(3,6),(4,6),(5,2)],7)
[1,1,3,2]=>[[4,3,1,1],[2]]=>([(0,4),(0,6),(1,3),(1,5),(3,6),(5,2)],7)
[1,1,4,1]=>[[4,4,1,1],[3]]=>([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7)
[1,1,5]=>[[5,1,1],[]]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>([(0,4),(0,6),(1,2),(1,5),(3,6),(5,3)],7)
[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
[1,2,1,3]=>[[4,2,2,1],[1,1]]=>([(0,4),(0,6),(1,3),(1,5),(3,6),(5,2)],7)
[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>([(0,5),(0,6),(1,4),(2,3),(2,5),(4,6)],7)
[1,2,2,2]=>[[4,3,2,1],[2,1]]=>([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5)],7)
[1,2,3,1]=>[[4,4,2,1],[3,1]]=>([(0,6),(1,3),(1,5),(2,4),(2,5),(4,6)],7)
[1,2,4]=>[[5,2,1],[1]]=>([(0,5),(0,6),(1,3),(1,6),(4,2),(5,4)],7)
[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>([(0,5),(1,2),(1,4),(3,6),(4,6),(5,3)],7)
[1,3,1,2]=>[[4,3,3,1],[2,2]]=>([(0,3),(0,5),(1,2),(1,4),(4,6),(5,6)],7)
[1,3,2,1]=>[[4,4,3,1],[3,2]]=>([(0,5),(1,5),(1,6),(2,3),(2,4),(4,6)],7)
[1,3,3]=>[[5,3,1],[2]]=>([(0,5),(0,6),(1,3),(1,4),(4,6),(5,2)],7)
[1,4,1,1]=>[[4,4,4,1],[3,3]]=>([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7)
[1,4,2]=>[[5,4,1],[3]]=>([(0,4),(0,6),(1,2),(1,5),(3,6),(5,3)],7)
[1,5,1]=>[[5,5,1],[4]]=>([(0,6),(1,2),(1,5),(3,6),(4,3),(5,4)],7)
[1,6]=>[[6,1],[]]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
[2,1,1,1,1,1]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>([(0,6),(1,2),(1,5),(3,6),(4,3),(5,4)],7)
[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>([(0,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7)
[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7)
[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7)
[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>([(0,6),(1,3),(1,5),(2,4),(2,5),(4,6)],7)
[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[2,1,4]=>[[5,2,2],[1,1]]=>([(0,6),(1,3),(1,5),(3,6),(4,2),(5,4)],7)
[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7)
[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>([(0,5),(1,5),(1,6),(2,3),(2,4),(4,6)],7)
[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7)
[2,2,3]=>[[5,3,2],[2,1]]=>([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4)],7)
[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6)],7)
[2,3,2]=>[[5,4,2],[3,1]]=>([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7)
[2,4,1]=>[[5,5,2],[4,1]]=>([(0,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7)
[2,5]=>[[6,2],[1]]=>([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7)
[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7)
[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6)],7)
[3,1,3]=>[[5,3,3],[2,2]]=>([(0,4),(1,3),(1,5),(3,6),(4,6),(5,2)],7)
[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>([(0,5),(0,6),(1,4),(2,3),(3,5),(4,6)],7)
[3,2,2]=>[[5,4,3],[3,2]]=>([(0,5),(0,6),(1,4),(2,3),(2,5),(4,6)],7)
[3,3,1]=>[[5,5,3],[4,2]]=>([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7)
[3,4]=>[[6,3],[2]]=>([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7)
[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[4,1,2]=>[[5,4,4],[3,3]]=>([(0,5),(1,2),(1,4),(3,6),(4,6),(5,3)],7)
[4,2,1]=>[[5,5,4],[4,3]]=>([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7)
[4,3]=>[[6,4],[3]]=>([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
[5,1,1]=>[[5,5,5],[4,4]]=>([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[5,2]=>[[6,5],[4]]=>([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
[6,1]=>[[6,6],[5]]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[7]=>[[7],[]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1],[]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1],[]]=>([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>([(0,7),(1,6),(1,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,1,3]=>[[3,1,1,1,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)
[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>([(0,3),(1,6),(1,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>([(0,6),(0,7),(1,3),(1,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,4]=>[[4,1,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)
[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>([(0,5),(1,6),(1,7),(3,7),(4,2),(5,3),(6,4)],8)
[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>([(0,6),(0,7),(1,3),(1,4),(4,7),(5,2),(6,5)],8)
[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>([(0,6),(1,3),(1,7),(2,6),(2,7),(3,5),(5,4)],8)
[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>([(0,4),(0,7),(1,3),(1,6),(3,7),(5,2),(6,5)],8)
[1,1,1,5]=>[[5,1,1,1],[]]=>([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8)
[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>([(0,5),(1,6),(1,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>([(0,6),(0,7),(1,3),(1,5),(4,7),(5,4),(6,2)],8)
[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>([(0,6),(1,4),(1,7),(2,3),(2,6),(3,7),(4,5)],8)
[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>([(0,6),(0,7),(1,3),(2,4),(2,6),(3,7),(4,5)],8)
[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>([(0,6),(0,7),(1,3),(1,6),(2,4),(2,7),(4,5)],8)
[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>([(0,7),(1,3),(1,6),(2,4),(2,6),(3,7),(4,5)],8)
[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>([(0,3),(0,4),(1,5),(1,6),(4,7),(5,7),(6,2)],8)
[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>([(0,6),(1,6),(1,7),(2,3),(2,4),(3,7),(4,5)],8)
[1,1,3,3]=>[[5,3,1,1],[2]]=>([(0,6),(0,7),(1,4),(1,5),(4,7),(5,3),(6,2)],8)
[1,1,6]=>[[6,1,1],[]]=>([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8)
[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>([(0,6),(1,3),(1,7),(2,7),(4,5),(5,2),(6,4)],8)
[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>([(0,4),(0,7),(1,2),(1,6),(3,7),(5,3),(6,5)],8)
[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>([(0,6),(1,4),(1,6),(2,3),(2,7),(4,5),(5,7)],8)
[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>([(0,5),(1,4),(1,7),(2,3),(2,6),(4,6),(5,7)],8)
[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>([(0,4),(0,7),(1,3),(1,6),(2,5),(2,6),(5,7)],8)
[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>([(0,6),(1,3),(1,7),(2,4),(2,5),(4,6),(5,7)],8)
[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>([(0,6),(0,7),(1,4),(2,3),(2,6),(4,5),(5,7)],8)
[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>([(0,6),(0,7),(1,4),(1,6),(2,3),(2,5),(5,7)],8)
[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>([(0,6),(1,5),(1,6),(2,5),(2,7),(3,4),(3,7)],8)
[1,2,2,3]=>[[5,3,2,1],[2,1]]=>([(0,6),(0,7),(1,3),(1,6),(2,4),(2,7),(4,5)],8)
[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>([(0,5),(1,4),(1,6),(2,3),(2,6),(4,7),(5,7)],8)
[1,2,3,2]=>[[5,4,2,1],[3,1]]=>([(0,4),(0,7),(1,3),(1,6),(2,5),(2,6),(5,7)],8)
[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>([(0,3),(0,5),(1,4),(1,6),(2,7),(5,7),(6,2)],8)
[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(4,7),(5,7)],8)
[1,3,1,3]=>[[5,3,3,1],[2,2]]=>([(0,3),(0,4),(1,5),(1,6),(4,7),(5,7),(6,2)],8)
[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>([(0,6),(0,7),(1,5),(2,3),(2,4),(4,6),(5,7)],8)
[1,3,2,2]=>[[5,4,3,1],[3,2]]=>([(0,6),(0,7),(1,4),(1,6),(2,3),(2,5),(5,7)],8)
[1,3,3,1]=>[[5,5,3,1],[4,2]]=>([(0,6),(1,5),(1,7),(2,3),(2,4),(4,7),(5,6)],8)
[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>([(0,6),(1,2),(1,5),(3,7),(4,7),(5,4),(6,3)],8)
[1,4,1,2]=>[[5,4,4,1],[3,3]]=>([(0,3),(0,5),(1,4),(1,6),(2,7),(5,7),(6,2)],8)
[1,4,2,1]=>[[5,5,4,1],[4,3]]=>([(0,6),(1,6),(1,7),(2,3),(2,4),(4,5),(5,7)],8)
[1,4,3]=>[[6,4,1],[3]]=>([(0,6),(0,7),(1,3),(1,5),(4,7),(5,4),(6,2)],8)
[1,7]=>[[7,1],[]]=>([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
[2,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2],[1,1,1,1,1,1]]=>([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>([(0,7),(1,2),(1,6),(3,7),(4,5),(5,3),(6,4)],8)
[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>([(0,7),(1,6),(2,3),(2,6),(3,5),(4,7),(5,4)],8)
[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>([(0,6),(1,3),(2,4),(2,7),(3,7),(4,5),(5,6)],8)
[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>([(0,7),(1,3),(1,6),(2,4),(2,6),(4,5),(5,7)],8)
[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>([(0,7),(1,6),(2,3),(2,4),(3,7),(4,5),(5,6)],8)
[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>([(0,7),(1,4),(2,3),(2,6),(3,7),(4,5),(5,6)],8)
[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>([(0,6),(1,5),(1,7),(2,3),(2,4),(4,7),(5,6)],8)
[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>([(0,7),(1,5),(2,5),(2,6),(3,4),(3,6),(4,7)],8)
[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>([(0,7),(1,3),(1,6),(2,4),(2,6),(3,7),(4,5)],8)
[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>([(0,6),(1,4),(2,3),(2,5),(3,7),(4,7),(5,6)],8)
[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>([(0,6),(1,3),(1,7),(2,4),(2,5),(4,6),(5,7)],8)
[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>([(0,3),(1,6),(2,6),(2,7),(3,5),(4,7),(5,4)],8)
[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>([(0,6),(1,6),(1,7),(2,3),(2,4),(4,5),(5,7)],8)
[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>([(0,5),(1,6),(2,5),(2,7),(3,4),(3,6),(4,7)],8)
[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>([(0,6),(1,6),(1,7),(2,3),(2,4),(3,7),(4,5)],8)
[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>([(0,5),(1,6),(1,7),(2,5),(2,6),(3,4),(4,7)],8)
[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>([(0,6),(1,5),(1,6),(2,5),(2,7),(3,4),(3,7)],8)
[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>([(0,7),(1,5),(2,5),(2,6),(3,4),(3,6),(4,7)],8)
[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>([(0,6),(1,4),(2,3),(2,6),(3,7),(4,5),(5,7)],8)
[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(4,7),(5,7)],8)
[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>([(0,5),(1,6),(2,5),(2,7),(3,4),(3,6),(4,7)],8)
[2,3,3]=>[[6,4,2],[3,1]]=>([(0,6),(1,4),(1,7),(2,3),(2,6),(3,7),(4,5)],8)
[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>([(0,6),(1,3),(2,4),(2,6),(3,7),(4,5),(5,7)],8)
[2,4,2]=>[[6,5,2],[4,1]]=>([(0,6),(1,4),(1,6),(2,3),(2,7),(4,5),(5,7)],8)
[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>([(0,6),(1,3),(2,4),(2,6),(3,7),(4,5),(5,7)],8)
[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>([(0,4),(1,5),(1,6),(3,7),(4,7),(5,2),(6,3)],8)
[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>([(0,3),(1,5),(2,4),(2,6),(3,7),(4,7),(5,6)],8)
[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>([(0,5),(1,4),(1,6),(2,3),(2,6),(4,7),(5,7)],8)
[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>([(0,6),(1,4),(2,3),(2,5),(3,7),(4,7),(5,6)],8)
[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>([(0,6),(0,7),(1,3),(2,4),(3,7),(4,5),(5,6)],8)
[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>([(0,6),(0,7),(1,5),(2,3),(2,4),(4,6),(5,7)],8)
[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>([(0,5),(1,6),(1,7),(2,5),(2,6),(3,4),(4,7)],8)
[3,2,3]=>[[6,4,3],[3,2]]=>([(0,6),(0,7),(1,3),(2,4),(2,6),(3,7),(4,5)],8)
[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>([(0,3),(1,5),(2,4),(2,6),(3,7),(4,7),(5,6)],8)
[3,3,2]=>[[6,5,3],[4,2]]=>([(0,5),(1,4),(1,7),(2,3),(2,6),(4,6),(5,7)],8)
[3,4,1]=>[[6,6,3],[5,2]]=>([(0,6),(1,3),(2,4),(2,7),(3,7),(4,5),(5,6)],8)
[4,1,1,1,1]=>[[4,4,4,4,4],[3,3,3,3]]=>([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>([(0,6),(1,2),(1,5),(3,7),(4,7),(5,4),(6,3)],8)
[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>([(0,6),(1,4),(2,3),(2,6),(3,7),(4,5),(5,7)],8)
[4,1,3]=>[[6,4,4],[3,3]]=>([(0,6),(1,4),(1,5),(3,7),(4,7),(5,2),(6,3)],8)
[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>([(0,6),(0,7),(1,3),(2,4),(3,7),(4,5),(5,6)],8)
[4,2,2]=>[[6,5,4],[4,3]]=>([(0,6),(0,7),(1,4),(2,3),(2,6),(4,5),(5,7)],8)
[4,3,1]=>[[6,6,4],[5,3]]=>([(0,7),(1,4),(2,3),(2,6),(3,7),(4,5),(5,6)],8)
[4,4]=>[[7,4],[3]]=>([(0,5),(1,6),(1,7),(3,7),(4,2),(5,3),(6,4)],8)
[5,1,1,1]=>[[5,5,5,5],[4,4,4]]=>([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[6,1,1]=>[[6,6,6],[5,5]]=>([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[7,1]=>[[7,7],[6]]=>([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[8]=>[[8],[]]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1,1],[]]=>([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1,1],[]]=>([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,3]=>[[3,1,1,1,1,1,1],[]]=>([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)
[1,1,1,1,1,4]=>[[4,1,1,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)
[1,1,1,1,5]=>[[5,1,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9)
[1,1,1,6]=>[[6,1,1,1],[]]=>([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9)
[1,1,7]=>[[7,1,1],[]]=>([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9)
[1,8]=>[[8,1],[]]=>([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9)
[2,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]=>([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[3,1,1,1,1,1,1]=>[[3,3,3,3,3,3,3],[2,2,2,2,2,2]]=>([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[4,1,1,1,1,1]=>[[4,4,4,4,4,4],[3,3,3,3,3]]=>([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[5,1,1,1,1]=>[[5,5,5,5,5],[4,4,4,4]]=>([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[6,1,1,1]=>[[6,6,6,6],[5,5,5]]=>([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[7,1,1]=>[[7,7,7],[6,6]]=>([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[8,1]=>[[8,8],[7]]=>([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[9]=>[[9],[]]=>([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1,1,1],[]]=>([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1,1,1],[]]=>([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,1,3]=>[[3,1,1,1,1,1,1,1],[]]=>([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10)
[1,1,1,1,1,1,4]=>[[4,1,1,1,1,1,1],[]]=>([(0,8),(0,9),(3,4),(4,6),(5,3),(6,2),(7,1),(8,7),(9,5)],10)
[1,1,1,1,1,5]=>[[5,1,1,1,1,1],[]]=>([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10)
[1,1,1,1,6]=>[[6,1,1,1,1],[]]=>([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10)
[1,1,1,7]=>[[7,1,1,1],[]]=>([(0,8),(0,9),(3,4),(4,6),(5,3),(6,2),(7,1),(8,7),(9,5)],10)
[1,1,8]=>[[8,1,1],[]]=>([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10)
[1,9]=>[[9,1],[]]=>([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[2,1,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]=>([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[3,1,1,1,1,1,1,1]=>[[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]]=>([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[4,1,1,1,1,1,1]=>[[4,4,4,4,4,4,4],[3,3,3,3,3,3]]=>([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[5,1,1,1,1,1]=>[[5,5,5,5,5,5],[4,4,4,4,4]]=>([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[6,1,1,1,1]=>[[6,6,6,6,6],[5,5,5,5]]=>([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[7,1,1,1]=>[[7,7,7,7],[6,6,6]]=>([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[8,1,1]=>[[8,8,8],[7,7]]=>([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[9,1]=>[[9,9],[8]]=>([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[10]=>[[10],[]]=>([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
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.
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.
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