Identifier
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Images
=>
Cc0028;cc-rep-1Cc0029;cc-rep-2
[1]=>[[1],[]]=>([],1) [1,1]=>[[1,1],[]]=>([],1) [2]=>[[2],[]]=>([],1) [1,1,1]=>[[1,1,1],[]]=>([],1) [1,2]=>[[2,1],[]]=>([],1) [2,1]=>[[2,2],[1]]=>([],1) [3]=>[[3],[]]=>([],1) [1,1,1,1]=>[[1,1,1,1],[]]=>([],1) [1,1,2]=>[[2,1,1],[]]=>([],1) [1,2,1]=>[[2,2,1],[1]]=>([(0,1)],2) [1,3]=>[[3,1],[]]=>([],1) [2,1,1]=>[[2,2,2],[1,1]]=>([],1) [2,2]=>[[3,2],[1]]=>([(0,1)],2) [3,1]=>[[3,3],[2]]=>([],1) [4]=>[[4],[]]=>([],1) [1,1,1,1,1]=>[[1,1,1,1,1],[]]=>([],1) [1,1,1,2]=>[[2,1,1,1],[]]=>([],1) [1,1,2,1]=>[[2,2,1,1],[1]]=>([(0,1)],2) [1,1,3]=>[[3,1,1],[]]=>([],1) [1,2,1,1]=>[[2,2,2,1],[1,1]]=>([(0,1)],2) [1,2,2]=>[[3,2,1],[1]]=>([(0,2),(2,1)],3) [1,3,1]=>[[3,3,1],[2]]=>([(0,1)],2) [1,4]=>[[4,1],[]]=>([],1) [2,1,1,1]=>[[2,2,2,2],[1,1,1]]=>([],1) [2,1,2]=>[[3,2,2],[1,1]]=>([(0,1)],2) [2,2,1]=>[[3,3,2],[2,1]]=>([(0,2),(2,1)],3) [2,3]=>[[4,2],[1]]=>([(0,1)],2) [3,1,1]=>[[3,3,3],[2,2]]=>([],1) [3,2]=>[[4,3],[2]]=>([(0,1)],2) [4,1]=>[[4,4],[3]]=>([],1) [5]=>[[5],[]]=>([],1) [1,1,1,1,1,1]=>[[1,1,1,1,1,1],[]]=>([],1) [1,1,1,1,2]=>[[2,1,1,1,1],[]]=>([],1) [1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>([(0,1)],2) [1,1,1,3]=>[[3,1,1,1],[]]=>([],1) [1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>([(0,2),(2,1)],3) [1,1,2,2]=>[[3,2,1,1],[1]]=>([(0,2),(2,1)],3) [1,1,3,1]=>[[3,3,1,1],[2]]=>([(0,1)],2) [1,1,4]=>[[4,1,1],[]]=>([],1) [1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>([(0,1)],2) [1,2,1,2]=>[[3,2,2,1],[1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [1,2,2,1]=>[[3,3,2,1],[2,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [1,2,3]=>[[4,2,1],[1]]=>([(0,2),(2,1)],3) [1,3,1,1]=>[[3,3,3,1],[2,2]]=>([(0,1)],2) [1,3,2]=>[[4,3,1],[2]]=>([(0,1),(0,2),(1,3),(2,3)],4) [1,4,1]=>[[4,4,1],[3]]=>([(0,1)],2) [1,5]=>[[5,1],[]]=>([],1) [2,1,1,1,1]=>[[2,2,2,2,2],[1,1,1,1]]=>([],1) [2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>([(0,1)],2) [2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [2,1,3]=>[[4,2,2],[1,1]]=>([(0,1)],2) [2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>([(0,2),(2,1)],3) [2,2,2]=>[[4,3,2],[2,1]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [2,3,1]=>[[4,4,2],[3,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [2,4]=>[[5,2],[1]]=>([(0,1)],2) [3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>([],1) [3,1,2]=>[[4,3,3],[2,2]]=>([(0,1)],2) [3,2,1]=>[[4,4,3],[3,2]]=>([(0,2),(2,1)],3) [3,3]=>[[5,3],[2]]=>([(0,2),(2,1)],3) [4,1,1]=>[[4,4,4],[3,3]]=>([],1) [4,2]=>[[5,4],[3]]=>([(0,1)],2) [5,1]=>[[5,5],[4]]=>([],1) [6]=>[[6],[]]=>([],1) [1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1],[]]=>([],1) [1,1,1,1,1,2]=>[[2,1,1,1,1,1],[]]=>([],1) [1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>([(0,1)],2) [1,1,1,1,3]=>[[3,1,1,1,1],[]]=>([],1) [1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>([(0,2),(2,1)],3) [1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>([(0,2),(2,1)],3) [1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>([(0,1)],2) [1,1,1,4]=>[[4,1,1,1],[]]=>([],1) [1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>([(0,2),(2,1)],3) [1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [1,1,2,3]=>[[4,2,1,1],[1]]=>([(0,2),(2,1)],3) [1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>([(0,2),(2,1)],3) [1,1,3,2]=>[[4,3,1,1],[2]]=>([(0,1),(0,2),(1,3),(2,3)],4) [1,1,4,1]=>[[4,4,1,1],[3]]=>([(0,1)],2) [1,1,5]=>[[5,1,1],[]]=>([],1) [1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>([(0,1)],2) [1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [1,2,1,3]=>[[4,2,2,1],[1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [1,2,2,2]=>[[4,3,2,1],[2,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [1,2,3,1]=>[[4,4,2,1],[3,1]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) [1,2,4]=>[[5,2,1],[1]]=>([(0,2),(2,1)],3) [1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>([(0,1)],2) [1,3,1,2]=>[[4,3,3,1],[2,2]]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5) [1,3,2,1]=>[[4,4,3,1],[3,2]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) [1,3,3]=>[[5,3,1],[2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [1,4,1,1]=>[[4,4,4,1],[3,3]]=>([(0,1)],2) [1,4,2]=>[[5,4,1],[3]]=>([(0,1),(0,2),(1,3),(2,3)],4) [1,5,1]=>[[5,5,1],[4]]=>([(0,1)],2) [1,6]=>[[6,1],[]]=>([],1) [2,1,1,1,1,1]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>([],1) [2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>([(0,1)],2) [2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>([(0,1)],2) [2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5) [2,1,4]=>[[5,2,2],[1,1]]=>([(0,1)],2) [2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>([(0,2),(2,1)],3) [2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [2,2,3]=>[[5,3,2],[2,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [2,3,2]=>[[5,4,2],[3,1]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [2,4,1]=>[[5,5,2],[4,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [2,5]=>[[6,2],[1]]=>([(0,1)],2) [3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>([],1) [3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>([(0,1)],2) [3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>([(0,1),(0,2),(1,3),(2,3)],4) [3,1,3]=>[[5,3,3],[2,2]]=>([(0,2),(2,1)],3) [3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>([(0,2),(2,1)],3) [3,2,2]=>[[5,4,3],[3,2]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [3,3,1]=>[[5,5,3],[4,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [3,4]=>[[6,3],[2]]=>([(0,2),(2,1)],3) [4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>([],1) [4,1,2]=>[[5,4,4],[3,3]]=>([(0,1)],2) [4,2,1]=>[[5,5,4],[4,3]]=>([(0,2),(2,1)],3) [4,3]=>[[6,4],[3]]=>([(0,2),(2,1)],3) [5,1,1]=>[[5,5,5],[4,4]]=>([],1) [5,2]=>[[6,5],[4]]=>([(0,1)],2) [6,1]=>[[6,6],[5]]=>([],1) [7]=>[[7],[]]=>([],1) [1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1],[]]=>([],1) [1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1],[]]=>([],1) [1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>([(0,1)],2) [1,1,1,1,1,3]=>[[3,1,1,1,1,1],[]]=>([],1) [1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>([(0,2),(2,1)],3) [1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>([(0,2),(2,1)],3) [1,1,1,1,4]=>[[4,1,1,1,1],[]]=>([],1) [1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>([(0,3),(2,1),(3,2)],4) [1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>([(0,1),(0,2),(1,3),(2,3)],4) [1,1,1,5]=>[[5,1,1,1],[]]=>([],1) [1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>([(0,2),(2,1)],3) [1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) [1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) [1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9) [1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) [1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) [1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) [1,1,3,3]=>[[5,3,1,1],[2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [1,1,6]=>[[6,1,1],[]]=>([],1) [1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>([(0,1)],2) [1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) [1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) [1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>([(0,6),(1,9),(2,8),(3,7),(4,3),(4,8),(5,1),(5,7),(6,2),(6,4),(7,9),(8,5)],10) [1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) [1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>([(0,6),(1,9),(2,8),(3,7),(4,3),(4,8),(5,1),(5,7),(6,2),(6,4),(7,9),(8,5)],10) [1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>([(0,6),(1,10),(2,9),(3,8),(4,3),(4,9),(5,1),(5,8),(6,7),(7,2),(7,4),(8,10),(9,5)],11) [1,2,2,3]=>[[5,3,2,1],[2,1]]=>([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9) [1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) [1,2,3,2]=>[[5,4,2,1],[3,1]]=>([(0,4),(0,6),(2,9),(3,8),(4,7),(5,2),(5,8),(6,3),(6,7),(7,5),(8,9),(9,1)],10) [1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5) [1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>([(0,5),(1,7),(2,6),(3,6),(4,3),(4,7),(5,1),(5,4),(7,2)],8) [1,3,1,3]=>[[5,3,3,1],[2,2]]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) [1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) [1,3,2,2]=>[[5,4,3,1],[3,2]]=>([(0,4),(0,6),(2,9),(3,8),(4,7),(5,2),(5,8),(6,3),(6,7),(7,5),(8,9),(9,1)],10) [1,3,3,1]=>[[5,5,3,1],[4,2]]=>([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9) [1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>([(0,1)],2) [1,4,1,2]=>[[5,4,4,1],[3,3]]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5) [1,4,2,1]=>[[5,5,4,1],[4,3]]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) [1,4,3]=>[[6,4,1],[3]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [1,7]=>[[7,1],[]]=>([],1) [2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>([(0,1)],2) [2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5) [2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>([(0,3),(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,2),(5,6),(6,4),(7,8)],9) [2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>([(0,6),(1,9),(2,8),(3,7),(4,3),(4,8),(5,1),(5,7),(6,2),(6,4),(7,9),(8,5)],10) [2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) [2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) [2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) [2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>([(0,2),(2,1)],3) [2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>([(0,6),(1,9),(2,8),(3,7),(4,3),(4,8),(5,1),(5,7),(6,2),(6,4),(7,9),(8,5)],10) [2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) [2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>([(0,6),(1,8),(2,7),(4,7),(5,2),(5,8),(6,1),(6,5),(7,3),(8,4)],9) [2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>([(0,4),(0,7),(1,10),(3,8),(4,9),(5,2),(6,1),(6,8),(7,3),(7,9),(8,10),(9,6),(10,5)],11) [2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>([(0,4),(0,6),(2,9),(3,8),(4,7),(5,2),(5,8),(6,3),(6,7),(7,5),(8,9),(9,1)],10) [2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) [2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>([(0,4),(0,6),(2,9),(3,8),(4,7),(5,2),(5,8),(6,3),(6,7),(7,5),(8,9),(9,1)],10) [2,3,3]=>[[6,4,2],[3,1]]=>([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) [2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>([(0,1),(0,2),(1,3),(2,3)],4) [2,4,2]=>[[6,5,2],[4,1]]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) [3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>([(0,1),(0,2),(1,3),(2,3)],4) [3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>([(0,2),(2,1)],3) [3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>([(0,3),(0,5),(2,7),(3,6),(4,2),(4,6),(5,4),(6,7),(7,1)],8) [3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) [3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>([(0,2),(2,1)],3) [3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) [3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>([(0,6),(1,8),(3,7),(4,5),(5,1),(5,7),(6,3),(6,4),(7,8),(8,2)],9) [3,2,3]=>[[6,4,3],[3,2]]=>([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) [3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [3,3,2]=>[[6,5,3],[4,2]]=>([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) [3,4,1]=>[[6,6,3],[5,2]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [4,1,1,1,1]=>[[4,4,4,4,4],[3,3,3,3]]=>([],1) [4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>([(0,1)],2) [4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>([(0,1),(0,2),(1,3),(2,3)],4) [4,1,3]=>[[6,4,4],[3,3]]=>([(0,2),(2,1)],3) [4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>([(0,2),(2,1)],3) [4,2,2]=>[[6,5,4],[4,3]]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [4,3,1]=>[[6,6,4],[5,3]]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [4,4]=>[[7,4],[3]]=>([(0,3),(2,1),(3,2)],4) [8]=>[[8],[]]=>([],1) [1,1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1,1],[]]=>([],1) [1,1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1,1],[]]=>([],1) [1,1,1,1,1,1,3]=>[[3,1,1,1,1,1,1],[]]=>([],1) [1,1,1,1,1,4]=>[[4,1,1,1,1,1],[]]=>([],1) [1,1,1,1,5]=>[[5,1,1,1,1],[]]=>([],1) [1,1,1,6]=>[[6,1,1,1],[]]=>([],1) [1,1,7]=>[[7,1,1],[]]=>([],1) [1,8]=>[[8,1],[]]=>([],1) [9]=>[[9],[]]=>([],1) [1,1,1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1,1,1],[]]=>([],1) [1,1,1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1,1,1],[]]=>([],1) [1,1,1,1,1,1,1,3]=>[[3,1,1,1,1,1,1,1],[]]=>([],1) [1,1,1,1,1,1,4]=>[[4,1,1,1,1,1,1],[]]=>([],1) [1,1,1,1,1,5]=>[[5,1,1,1,1,1],[]]=>([],1) [1,1,1,1,6]=>[[6,1,1,1,1],[]]=>([],1) [1,1,1,7]=>[[7,1,1,1],[]]=>([],1) [1,1,8]=>[[8,1,1],[]]=>([],1) [1,9]=>[[9,1],[]]=>([],1) [10]=>[[10],[]]=>([],1)
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.
Map
dominating sublattice
Description
Return the sublattice of the dominance order induced by the support of the expansion of the skew Schur function into Schur functions.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the subposet of the dominance order whose elements are the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a lattice.
The example $\lambda = (5^2,4^2,1)$ and $\mu=(3,2)$ shows that this lattice is not a sublattice of the dominance order.