Identifier
-
Mp00185:
Skew partitions
—cell poset⟶
Posets
St001633: Posets ⟶ ℤ
Values
=>
Cc0028;cc-rep-0
Cc0014;cc-rep
[[1],[]]=>([],1)=>0
[[2],[]]=>([(0,1)],2)=>0
[[1,1],[]]=>([(0,1)],2)=>0
[[2,1],[1]]=>([],2)=>0
[[3],[]]=>([(0,2),(2,1)],3)=>0
[[2,1],[]]=>([(0,1),(0,2)],3)=>0
[[3,1],[1]]=>([(1,2)],3)=>0
[[2,2],[1]]=>([(0,2),(1,2)],3)=>0
[[3,2],[2]]=>([(1,2)],3)=>0
[[1,1,1],[]]=>([(0,2),(2,1)],3)=>0
[[2,2,1],[1,1]]=>([(1,2)],3)=>0
[[2,1,1],[1]]=>([(1,2)],3)=>0
[[3,2,1],[2,1]]=>([],3)=>0
[[4],[]]=>([(0,3),(2,1),(3,2)],4)=>0
[[3,1],[]]=>([(0,2),(0,3),(3,1)],4)=>0
[[4,1],[1]]=>([(1,2),(2,3)],4)=>0
[[2,2],[]]=>([(0,1),(0,2),(1,3),(2,3)],4)=>1
[[3,2],[1]]=>([(0,3),(1,2),(1,3)],4)=>0
[[4,2],[2]]=>([(0,3),(1,2)],4)=>0
[[2,1,1],[]]=>([(0,2),(0,3),(3,1)],4)=>0
[[3,2,1],[1,1]]=>([(1,2),(1,3)],4)=>0
[[3,1,1],[1]]=>([(0,3),(1,2)],4)=>0
[[4,2,1],[2,1]]=>([(2,3)],4)=>0
[[3,3],[2]]=>([(0,3),(1,2),(2,3)],4)=>0
[[4,3],[3]]=>([(1,2),(2,3)],4)=>0
[[2,2,1],[1]]=>([(0,3),(1,2),(1,3)],4)=>0
[[3,3,1],[2,1]]=>([(1,3),(2,3)],4)=>0
[[3,2,1],[2]]=>([(1,2),(1,3)],4)=>0
[[4,3,1],[3,1]]=>([(2,3)],4)=>0
[[2,2,2],[1,1]]=>([(0,3),(1,2),(2,3)],4)=>0
[[3,3,2],[2,2]]=>([(0,3),(1,2)],4)=>0
[[3,2,2],[2,1]]=>([(1,3),(2,3)],4)=>0
[[4,3,2],[3,2]]=>([(2,3)],4)=>0
[[1,1,1,1],[]]=>([(0,3),(2,1),(3,2)],4)=>0
[[2,2,2,1],[1,1,1]]=>([(1,2),(2,3)],4)=>0
[[2,2,1,1],[1,1]]=>([(0,3),(1,2)],4)=>0
[[3,3,2,1],[2,2,1]]=>([(2,3)],4)=>0
[[2,1,1,1],[1]]=>([(1,2),(2,3)],4)=>0
[[3,2,2,1],[2,1,1]]=>([(2,3)],4)=>0
[[3,2,1,1],[2,1]]=>([(2,3)],4)=>0
[[4,3,2,1],[3,2,1]]=>([],4)=>0
[[5],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>0
[[4,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>0
[[5,1],[1]]=>([(1,4),(3,2),(4,3)],5)=>0
[[3,2],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>1
[[4,2],[1]]=>([(0,4),(1,2),(1,4),(2,3)],5)=>0
[[5,2],[2]]=>([(0,3),(1,4),(4,2)],5)=>0
[[3,1,1],[]]=>([(0,3),(0,4),(3,2),(4,1)],5)=>0
[[4,2,1],[1,1]]=>([(1,3),(1,4),(4,2)],5)=>0
[[4,1,1],[1]]=>([(0,3),(1,4),(4,2)],5)=>0
[[5,2,1],[2,1]]=>([(2,3),(3,4)],5)=>0
[[3,3],[1]]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>1
[[4,3],[2]]=>([(0,3),(1,2),(1,4),(3,4)],5)=>0
[[5,3],[3]]=>([(0,3),(1,4),(4,2)],5)=>0
[[2,2,1],[]]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>1
[[3,3,1],[1,1]]=>([(1,2),(1,3),(2,4),(3,4)],5)=>1
[[3,2,1],[1]]=>([(0,3),(0,4),(1,2),(1,4)],5)=>0
[[4,3,1],[2,1]]=>([(1,4),(2,3),(2,4)],5)=>0
[[4,2,1],[2]]=>([(0,4),(1,2),(1,3)],5)=>0
[[5,3,1],[3,1]]=>([(1,4),(2,3)],5)=>0
[[3,2,2],[1,1]]=>([(0,4),(1,2),(1,3),(3,4)],5)=>0
[[4,3,2],[2,2]]=>([(0,4),(1,2),(1,3)],5)=>0
[[4,2,2],[2,1]]=>([(0,4),(1,4),(2,3)],5)=>0
[[5,3,2],[3,2]]=>([(1,4),(2,3)],5)=>0
[[2,1,1,1],[]]=>([(0,2),(0,4),(3,1),(4,3)],5)=>0
[[3,2,2,1],[1,1,1]]=>([(1,3),(1,4),(4,2)],5)=>0
[[3,2,1,1],[1,1]]=>([(0,4),(1,2),(1,3)],5)=>0
[[4,3,2,1],[2,2,1]]=>([(2,3),(2,4)],5)=>0
[[3,1,1,1],[1]]=>([(0,3),(1,4),(4,2)],5)=>0
[[4,2,2,1],[2,1,1]]=>([(1,4),(2,3)],5)=>0
[[4,2,1,1],[2,1]]=>([(1,4),(2,3)],5)=>0
[[5,3,2,1],[3,2,1]]=>([(3,4)],5)=>0
[[4,4],[3]]=>([(0,4),(1,2),(2,3),(3,4)],5)=>0
[[5,4],[4]]=>([(1,4),(3,2),(4,3)],5)=>0
[[3,3,1],[2]]=>([(0,4),(1,2),(1,3),(3,4)],5)=>0
[[4,4,1],[3,1]]=>([(1,4),(2,3),(3,4)],5)=>0
[[4,3,1],[3]]=>([(1,3),(1,4),(4,2)],5)=>0
[[5,4,1],[4,1]]=>([(2,3),(3,4)],5)=>0
[[2,2,2],[1]]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>1
[[3,3,2],[2,1]]=>([(0,4),(1,3),(2,3),(2,4)],5)=>0
[[4,4,2],[3,2]]=>([(0,4),(1,4),(2,3)],5)=>0
[[3,2,2],[2]]=>([(1,2),(1,3),(2,4),(3,4)],5)=>1
[[4,3,2],[3,1]]=>([(1,4),(2,3),(2,4)],5)=>0
[[5,4,2],[4,2]]=>([(1,4),(2,3)],5)=>0
[[2,2,1,1],[1]]=>([(0,4),(1,2),(1,4),(2,3)],5)=>0
[[3,3,2,1],[2,1,1]]=>([(1,4),(2,3),(2,4)],5)=>0
[[3,3,1,1],[2,1]]=>([(0,4),(1,4),(2,3)],5)=>0
[[4,4,2,1],[3,2,1]]=>([(2,4),(3,4)],5)=>0
[[3,2,1,1],[2]]=>([(1,3),(1,4),(4,2)],5)=>0
[[4,3,2,1],[3,1,1]]=>([(2,3),(2,4)],5)=>0
[[4,3,1,1],[3,1]]=>([(1,4),(2,3)],5)=>0
[[5,4,2,1],[4,2,1]]=>([(3,4)],5)=>0
[[3,3,3],[2,2]]=>([(0,3),(1,2),(2,4),(3,4)],5)=>0
[[4,4,3],[3,3]]=>([(0,3),(1,4),(4,2)],5)=>0
[[4,3,3],[3,2]]=>([(1,4),(2,3),(3,4)],5)=>0
[[5,4,3],[4,3]]=>([(2,3),(3,4)],5)=>0
[[2,2,2,1],[1,1]]=>([(0,3),(1,2),(1,4),(3,4)],5)=>0
[[3,3,3,1],[2,2,1]]=>([(1,4),(2,3),(3,4)],5)=>0
[[3,3,2,1],[2,2]]=>([(0,4),(1,2),(1,3)],5)=>0
[[4,4,3,1],[3,3,1]]=>([(1,4),(2,3)],5)=>0
[[3,2,2,1],[2,1]]=>([(1,4),(2,3),(2,4)],5)=>0
[[4,3,3,1],[3,2,1]]=>([(2,4),(3,4)],5)=>0
[[4,3,2,1],[3,2]]=>([(2,3),(2,4)],5)=>0
[[5,4,3,1],[4,3,1]]=>([(3,4)],5)=>0
[[2,2,2,2],[1,1,1]]=>([(0,4),(1,2),(2,3),(3,4)],5)=>0
[[3,3,3,2],[2,2,2]]=>([(0,3),(1,4),(4,2)],5)=>0
[[3,3,2,2],[2,2,1]]=>([(0,4),(1,4),(2,3)],5)=>0
[[4,4,3,2],[3,3,2]]=>([(1,4),(2,3)],5)=>0
[[3,2,2,2],[2,1,1]]=>([(1,4),(2,3),(3,4)],5)=>0
[[4,3,3,2],[3,2,2]]=>([(1,4),(2,3)],5)=>0
[[4,3,2,2],[3,2,1]]=>([(2,4),(3,4)],5)=>0
[[5,4,3,2],[4,3,2]]=>([(3,4)],5)=>0
[[1,1,1,1,1],[]]=>([(0,4),(2,3),(3,1),(4,2)],5)=>0
[[2,2,2,2,1],[1,1,1,1]]=>([(1,4),(3,2),(4,3)],5)=>0
[[2,2,2,1,1],[1,1,1]]=>([(0,3),(1,4),(4,2)],5)=>0
[[3,3,3,2,1],[2,2,2,1]]=>([(2,3),(3,4)],5)=>0
[[2,2,1,1,1],[1,1]]=>([(0,3),(1,4),(4,2)],5)=>0
[[3,3,2,2,1],[2,2,1,1]]=>([(1,4),(2,3)],5)=>0
[[3,3,2,1,1],[2,2,1]]=>([(1,4),(2,3)],5)=>0
[[4,4,3,2,1],[3,3,2,1]]=>([(3,4)],5)=>0
[[2,1,1,1,1],[1]]=>([(1,4),(3,2),(4,3)],5)=>0
[[3,2,2,2,1],[2,1,1,1]]=>([(2,3),(3,4)],5)=>0
[[3,2,2,1,1],[2,1,1]]=>([(1,4),(2,3)],5)=>0
[[4,3,3,2,1],[3,2,2,1]]=>([(3,4)],5)=>0
[[3,2,1,1,1],[2,1]]=>([(2,3),(3,4)],5)=>0
[[4,3,2,2,1],[3,2,1,1]]=>([(3,4)],5)=>0
[[4,3,2,1,1],[3,2,1]]=>([(3,4)],5)=>0
[[5,4,3,2,1],[4,3,2,1]]=>([],5)=>0
[[6],[]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>0
[[5,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>0
[[6,1],[1]]=>([(1,5),(3,4),(4,2),(5,3)],6)=>0
[[4,2],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>1
[[5,2],[1]]=>([(0,5),(1,4),(1,5),(3,2),(4,3)],6)=>0
[[6,2],[2]]=>([(0,5),(1,3),(4,2),(5,4)],6)=>0
[[4,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>0
[[5,2,1],[1,1]]=>([(1,3),(1,5),(4,2),(5,4)],6)=>0
[[5,1,1],[1]]=>([(0,5),(1,3),(4,2),(5,4)],6)=>0
[[6,2,1],[2,1]]=>([(2,3),(3,5),(5,4)],6)=>0
[[3,3],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[4,3],[1]]=>([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)=>1
[[5,3],[2]]=>([(0,3),(1,4),(1,5),(3,5),(4,2)],6)=>0
[[6,3],[3]]=>([(0,5),(1,4),(4,2),(5,3)],6)=>0
[[3,2,1],[]]=>([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)=>1
[[4,3,1],[1,1]]=>([(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>1
[[4,2,1],[1]]=>([(0,3),(0,5),(1,4),(1,5),(4,2)],6)=>0
[[5,3,1],[2,1]]=>([(1,5),(2,3),(2,5),(3,4)],6)=>0
[[5,2,1],[2]]=>([(0,5),(1,3),(1,4),(5,2)],6)=>0
[[6,3,1],[3,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[4,2,2],[1,1]]=>([(0,5),(1,3),(1,4),(3,5),(4,2)],6)=>0
[[5,3,2],[2,2]]=>([(0,4),(1,3),(1,5),(5,2)],6)=>0
[[5,2,2],[2,1]]=>([(0,5),(1,5),(2,3),(3,4)],6)=>0
[[6,3,2],[3,2]]=>([(1,3),(2,4),(4,5)],6)=>0
[[3,1,1,1],[]]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>0
[[4,2,2,1],[1,1,1]]=>([(1,4),(1,5),(4,3),(5,2)],6)=>0
[[4,2,1,1],[1,1]]=>([(0,4),(1,3),(1,5),(5,2)],6)=>0
[[5,3,2,1],[2,2,1]]=>([(2,3),(2,4),(4,5)],6)=>0
[[4,1,1,1],[1]]=>([(0,5),(1,4),(4,2),(5,3)],6)=>0
[[5,2,2,1],[2,1,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[5,2,1,1],[2,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[6,3,2,1],[3,2,1]]=>([(3,4),(4,5)],6)=>0
[[4,4],[2]]=>([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)=>1
[[5,4],[3]]=>([(0,4),(1,3),(1,5),(2,5),(4,2)],6)=>0
[[6,4],[4]]=>([(0,5),(1,3),(4,2),(5,4)],6)=>0
[[3,3,1],[1]]=>([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6)=>1
[[4,4,1],[2,1]]=>([(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1
[[4,3,1],[2]]=>([(0,4),(0,5),(1,2),(1,3),(3,5)],6)=>0
[[5,4,1],[3,1]]=>([(1,4),(2,3),(2,5),(4,5)],6)=>0
[[5,3,1],[3]]=>([(0,4),(1,3),(1,5),(5,2)],6)=>0
[[6,4,1],[4,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[2,2,2],[]]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[3,3,2],[1,1]]=>([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6)=>1
[[4,4,2],[2,2]]=>([(0,4),(1,2),(1,3),(2,5),(3,5)],6)=>1
[[3,2,2],[1]]=>([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6)=>1
[[4,3,2],[2,1]]=>([(0,4),(1,4),(1,5),(2,3),(2,5)],6)=>0
[[5,4,2],[3,2]]=>([(0,5),(1,3),(2,4),(2,5)],6)=>0
[[4,2,2],[2]]=>([(0,4),(1,2),(1,3),(2,5),(3,5)],6)=>1
[[5,3,2],[3,1]]=>([(0,5),(1,3),(2,4),(2,5)],6)=>0
[[6,4,2],[4,2]]=>([(0,5),(1,4),(2,3)],6)=>0
[[2,2,1,1],[]]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>1
[[3,3,2,1],[1,1,1]]=>([(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>1
[[3,3,1,1],[1,1]]=>([(0,4),(1,2),(1,3),(2,5),(3,5)],6)=>1
[[4,4,2,1],[2,2,1]]=>([(2,3),(2,4),(3,5),(4,5)],6)=>1
[[3,2,1,1],[1]]=>([(0,3),(0,5),(1,4),(1,5),(4,2)],6)=>0
[[4,3,2,1],[2,1,1]]=>([(1,4),(1,5),(2,3),(2,5)],6)=>0
[[4,3,1,1],[2,1]]=>([(0,5),(1,3),(2,4),(2,5)],6)=>0
[[5,4,2,1],[3,2,1]]=>([(2,5),(3,4),(3,5)],6)=>0
[[4,2,1,1],[2]]=>([(0,4),(1,3),(1,5),(5,2)],6)=>0
[[5,3,2,1],[3,1,1]]=>([(1,5),(2,3),(2,4)],6)=>0
[[5,3,1,1],[3,1]]=>([(0,5),(1,4),(2,3)],6)=>0
[[6,4,2,1],[4,2,1]]=>([(2,5),(3,4)],6)=>0
[[4,3,3],[2,2]]=>([(0,4),(1,2),(1,3),(3,5),(4,5)],6)=>0
[[5,4,3],[3,3]]=>([(0,5),(1,3),(1,4),(5,2)],6)=>0
[[5,3,3],[3,2]]=>([(0,5),(1,3),(2,4),(4,5)],6)=>0
[[6,4,3],[4,3]]=>([(1,3),(2,4),(4,5)],6)=>0
[[3,2,2,1],[1,1]]=>([(0,4),(0,5),(1,2),(1,3),(3,5)],6)=>0
[[4,3,3,1],[2,2,1]]=>([(1,5),(2,3),(2,4),(4,5)],6)=>0
[[4,3,2,1],[2,2]]=>([(0,4),(0,5),(1,2),(1,3)],6)=>0
[[5,4,3,1],[3,3,1]]=>([(1,5),(2,3),(2,4)],6)=>0
[[4,2,2,1],[2,1]]=>([(0,5),(1,3),(2,4),(2,5)],6)=>0
[[5,3,3,1],[3,2,1]]=>([(1,5),(2,5),(3,4)],6)=>0
[[5,3,2,1],[3,2]]=>([(1,5),(2,3),(2,4)],6)=>0
[[6,4,3,1],[4,3,1]]=>([(2,5),(3,4)],6)=>0
[[3,2,2,2],[1,1,1]]=>([(0,5),(1,2),(1,4),(3,5),(4,3)],6)=>0
[[4,3,3,2],[2,2,2]]=>([(0,4),(1,3),(1,5),(5,2)],6)=>0
[[4,3,2,2],[2,2,1]]=>([(0,5),(1,5),(2,3),(2,4)],6)=>0
[[5,4,3,2],[3,3,2]]=>([(1,5),(2,3),(2,4)],6)=>0
[[4,2,2,2],[2,1,1]]=>([(0,5),(1,3),(2,4),(4,5)],6)=>0
[[5,3,3,2],[3,2,2]]=>([(0,5),(1,4),(2,3)],6)=>0
[[5,3,2,2],[3,2,1]]=>([(1,5),(2,5),(3,4)],6)=>0
[[6,4,3,2],[4,3,2]]=>([(2,5),(3,4)],6)=>0
[[2,1,1,1,1],[]]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>0
[[3,2,2,2,1],[1,1,1,1]]=>([(1,3),(1,5),(4,2),(5,4)],6)=>0
[[3,2,2,1,1],[1,1,1]]=>([(0,4),(1,3),(1,5),(5,2)],6)=>0
[[4,3,3,2,1],[2,2,2,1]]=>([(2,3),(2,4),(4,5)],6)=>0
[[3,2,1,1,1],[1,1]]=>([(0,5),(1,3),(1,4),(5,2)],6)=>0
[[4,3,2,2,1],[2,2,1,1]]=>([(1,5),(2,3),(2,4)],6)=>0
[[4,3,2,1,1],[2,2,1]]=>([(1,5),(2,3),(2,4)],6)=>0
[[5,4,3,2,1],[3,3,2,1]]=>([(3,4),(3,5)],6)=>0
[[3,1,1,1,1],[1]]=>([(0,5),(1,3),(4,2),(5,4)],6)=>0
[[4,2,2,2,1],[2,1,1,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[4,2,2,1,1],[2,1,1]]=>([(0,5),(1,4),(2,3)],6)=>0
[[5,3,3,2,1],[3,2,2,1]]=>([(2,5),(3,4)],6)=>0
[[4,2,1,1,1],[2,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[5,3,2,2,1],[3,2,1,1]]=>([(2,5),(3,4)],6)=>0
[[5,3,2,1,1],[3,2,1]]=>([(2,5),(3,4)],6)=>0
[[6,4,3,2,1],[4,3,2,1]]=>([(4,5)],6)=>0
[[5,5],[4]]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>0
[[6,5],[5]]=>([(1,5),(3,4),(4,2),(5,3)],6)=>0
[[4,4,1],[3]]=>([(0,5),(1,2),(1,4),(3,5),(4,3)],6)=>0
[[5,5,1],[4,1]]=>([(1,5),(2,3),(3,4),(4,5)],6)=>0
[[5,4,1],[4]]=>([(1,3),(1,5),(4,2),(5,4)],6)=>0
[[6,5,1],[5,1]]=>([(2,3),(3,5),(5,4)],6)=>0
[[3,3,2],[2]]=>([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6)=>1
[[4,4,2],[3,1]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>0
[[5,5,2],[4,2]]=>([(0,5),(1,3),(2,4),(4,5)],6)=>0
[[4,3,2],[3]]=>([(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>1
[[5,4,2],[4,1]]=>([(1,5),(2,3),(2,5),(3,4)],6)=>0
[[6,5,2],[5,2]]=>([(1,3),(2,4),(4,5)],6)=>0
[[3,3,1,1],[2]]=>([(0,5),(1,3),(1,4),(3,5),(4,2)],6)=>0
[[4,4,2,1],[3,1,1]]=>([(1,5),(2,3),(2,4),(4,5)],6)=>0
[[4,4,1,1],[3,1]]=>([(0,5),(1,3),(2,4),(4,5)],6)=>0
[[5,5,2,1],[4,2,1]]=>([(2,5),(3,4),(4,5)],6)=>0
[[4,3,1,1],[3]]=>([(1,4),(1,5),(4,3),(5,2)],6)=>0
[[5,4,2,1],[4,1,1]]=>([(2,3),(2,4),(4,5)],6)=>0
[[5,4,1,1],[4,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[6,5,2,1],[5,2,1]]=>([(3,4),(4,5)],6)=>0
[[3,3,3],[2,1]]=>([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)=>1
[[4,4,3],[3,2]]=>([(0,4),(1,4),(1,5),(2,3),(3,5)],6)=>0
[[5,5,3],[4,3]]=>([(0,5),(1,5),(2,3),(3,4)],6)=>0
[[4,3,3],[3,1]]=>([(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1
[[5,4,3],[4,2]]=>([(1,4),(2,3),(2,5),(4,5)],6)=>0
[[6,5,3],[5,3]]=>([(1,3),(2,4),(4,5)],6)=>0
[[2,2,2,1],[1]]=>([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)=>1
[[3,3,3,1],[2,1,1]]=>([(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1
[[3,3,2,1],[2,1]]=>([(0,4),(1,4),(1,5),(2,3),(2,5)],6)=>0
[[4,4,3,1],[3,2,1]]=>([(1,5),(2,4),(3,4),(3,5)],6)=>0
[[4,4,2,1],[3,2]]=>([(0,5),(1,5),(2,3),(2,4)],6)=>0
[[5,5,3,1],[4,3,1]]=>([(1,5),(2,5),(3,4)],6)=>0
[[3,2,2,1],[2]]=>([(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>1
[[4,3,3,1],[3,1,1]]=>([(2,3),(2,4),(3,5),(4,5)],6)=>1
[[4,3,2,1],[3,1]]=>([(1,4),(1,5),(2,3),(2,5)],6)=>0
[[5,4,3,1],[4,2,1]]=>([(2,5),(3,4),(3,5)],6)=>0
[[5,4,2,1],[4,2]]=>([(1,5),(2,3),(2,4)],6)=>0
[[6,5,3,1],[5,3,1]]=>([(2,5),(3,4)],6)=>0
[[3,3,2,2],[2,1,1]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>0
[[4,4,3,2],[3,2,2]]=>([(0,5),(1,3),(2,4),(2,5)],6)=>0
[[4,4,2,2],[3,2,1]]=>([(0,5),(1,5),(2,4),(3,4)],6)=>0
[[5,5,3,2],[4,3,2]]=>([(1,5),(2,5),(3,4)],6)=>0
[[4,3,2,2],[3,1,1]]=>([(1,5),(2,3),(2,4),(4,5)],6)=>0
[[5,4,3,2],[4,2,2]]=>([(1,5),(2,3),(2,4)],6)=>0
[[5,4,2,2],[4,2,1]]=>([(1,5),(2,5),(3,4)],6)=>0
[[6,5,3,2],[5,3,2]]=>([(2,5),(3,4)],6)=>0
[[2,2,1,1,1],[1]]=>([(0,5),(1,4),(1,5),(3,2),(4,3)],6)=>0
[[3,3,2,2,1],[2,1,1,1]]=>([(1,5),(2,3),(2,5),(3,4)],6)=>0
[[3,3,2,1,1],[2,1,1]]=>([(0,5),(1,3),(2,4),(2,5)],6)=>0
[[4,4,3,2,1],[3,2,2,1]]=>([(2,5),(3,4),(3,5)],6)=>0
[[3,3,1,1,1],[2,1]]=>([(0,5),(1,5),(2,3),(3,4)],6)=>0
[[4,4,2,2,1],[3,2,1,1]]=>([(1,5),(2,5),(3,4)],6)=>0
[[4,4,2,1,1],[3,2,1]]=>([(1,5),(2,5),(3,4)],6)=>0
[[5,5,3,2,1],[4,3,2,1]]=>([(3,5),(4,5)],6)=>0
[[3,2,1,1,1],[2]]=>([(1,3),(1,5),(4,2),(5,4)],6)=>0
[[4,3,2,2,1],[3,1,1,1]]=>([(2,3),(2,4),(4,5)],6)=>0
[[4,3,2,1,1],[3,1,1]]=>([(1,5),(2,3),(2,4)],6)=>0
[[5,4,3,2,1],[4,2,2,1]]=>([(3,4),(3,5)],6)=>0
[[4,3,1,1,1],[3,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[5,4,2,2,1],[4,2,1,1]]=>([(2,5),(3,4)],6)=>0
[[5,4,2,1,1],[4,2,1]]=>([(2,5),(3,4)],6)=>0
[[6,5,3,2,1],[5,3,2,1]]=>([(4,5)],6)=>0
[[4,4,4],[3,3]]=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>0
[[5,5,4],[4,4]]=>([(0,5),(1,3),(4,2),(5,4)],6)=>0
[[5,4,4],[4,3]]=>([(1,5),(2,3),(3,4),(4,5)],6)=>0
[[6,5,4],[5,4]]=>([(2,3),(3,5),(5,4)],6)=>0
[[3,3,3,1],[2,2]]=>([(0,4),(1,2),(1,3),(3,5),(4,5)],6)=>0
[[4,4,4,1],[3,3,1]]=>([(1,4),(2,3),(3,5),(4,5)],6)=>0
[[4,4,3,1],[3,3]]=>([(0,4),(1,3),(1,5),(5,2)],6)=>0
[[5,5,4,1],[4,4,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[4,3,3,1],[3,2]]=>([(1,5),(2,3),(2,4),(4,5)],6)=>0
[[5,4,4,1],[4,3,1]]=>([(2,5),(3,4),(4,5)],6)=>0
[[5,4,3,1],[4,3]]=>([(2,3),(2,4),(4,5)],6)=>0
[[6,5,4,1],[5,4,1]]=>([(3,4),(4,5)],6)=>0
[[2,2,2,2],[1,1]]=>([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)=>1
[[3,3,3,2],[2,2,1]]=>([(0,4),(1,4),(1,5),(2,3),(3,5)],6)=>0
[[4,4,4,2],[3,3,2]]=>([(0,5),(1,3),(2,4),(4,5)],6)=>0
[[3,3,2,2],[2,2]]=>([(0,4),(1,2),(1,3),(2,5),(3,5)],6)=>1
[[4,4,3,2],[3,3,1]]=>([(0,5),(1,3),(2,4),(2,5)],6)=>0
[[5,5,4,2],[4,4,2]]=>([(0,5),(1,4),(2,3)],6)=>0
[[3,2,2,2],[2,1]]=>([(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1
[[4,3,3,2],[3,2,1]]=>([(1,5),(2,4),(3,4),(3,5)],6)=>0
[[5,4,4,2],[4,3,2]]=>([(1,5),(2,5),(3,4)],6)=>0
[[4,3,2,2],[3,2]]=>([(2,3),(2,4),(3,5),(4,5)],6)=>1
[[5,4,3,2],[4,3,1]]=>([(2,5),(3,4),(3,5)],6)=>0
[[6,5,4,2],[5,4,2]]=>([(2,5),(3,4)],6)=>0
[[2,2,2,1,1],[1,1]]=>([(0,3),(1,4),(1,5),(3,5),(4,2)],6)=>0
[[3,3,3,2,1],[2,2,1,1]]=>([(1,4),(2,3),(2,5),(4,5)],6)=>0
[[3,3,3,1,1],[2,2,1]]=>([(0,5),(1,3),(2,4),(4,5)],6)=>0
[[4,4,4,2,1],[3,3,2,1]]=>([(2,5),(3,4),(4,5)],6)=>0
[[3,3,2,1,1],[2,2]]=>([(0,4),(1,3),(1,5),(5,2)],6)=>0
[[4,4,3,2,1],[3,3,1,1]]=>([(1,5),(2,3),(2,4)],6)=>0
[[4,4,3,1,1],[3,3,1]]=>([(0,5),(1,4),(2,3)],6)=>0
[[5,5,4,2,1],[4,4,2,1]]=>([(2,5),(3,4)],6)=>0
[[3,2,2,1,1],[2,1]]=>([(1,5),(2,3),(2,5),(3,4)],6)=>0
[[4,3,3,2,1],[3,2,1,1]]=>([(2,5),(3,4),(3,5)],6)=>0
[[4,3,3,1,1],[3,2,1]]=>([(1,5),(2,5),(3,4)],6)=>0
[[5,4,4,2,1],[4,3,2,1]]=>([(3,5),(4,5)],6)=>0
[[4,3,2,1,1],[3,2]]=>([(2,3),(2,4),(4,5)],6)=>0
[[5,4,3,2,1],[4,3,1,1]]=>([(3,4),(3,5)],6)=>0
[[5,4,3,1,1],[4,3,1]]=>([(2,5),(3,4)],6)=>0
[[6,5,4,2,1],[5,4,2,1]]=>([(4,5)],6)=>0
[[3,3,3,3],[2,2,2]]=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>0
[[4,4,4,3],[3,3,3]]=>([(0,5),(1,4),(4,2),(5,3)],6)=>0
[[4,4,3,3],[3,3,2]]=>([(0,5),(1,3),(2,4),(4,5)],6)=>0
[[5,5,4,3],[4,4,3]]=>([(1,3),(2,4),(4,5)],6)=>0
[[4,3,3,3],[3,2,2]]=>([(1,4),(2,3),(3,5),(4,5)],6)=>0
[[5,4,4,3],[4,3,3]]=>([(1,3),(2,4),(4,5)],6)=>0
[[5,4,3,3],[4,3,2]]=>([(2,5),(3,4),(4,5)],6)=>0
[[6,5,4,3],[5,4,3]]=>([(3,4),(4,5)],6)=>0
[[2,2,2,2,1],[1,1,1]]=>([(0,4),(1,3),(1,5),(2,5),(4,2)],6)=>0
[[3,3,3,3,1],[2,2,2,1]]=>([(1,5),(2,3),(3,4),(4,5)],6)=>0
[[3,3,3,2,1],[2,2,2]]=>([(0,5),(1,3),(1,4),(5,2)],6)=>0
[[4,4,4,3,1],[3,3,3,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[3,3,2,2,1],[2,2,1]]=>([(0,5),(1,3),(2,4),(2,5)],6)=>0
[[4,4,3,3,1],[3,3,2,1]]=>([(1,5),(2,5),(3,4)],6)=>0
[[4,4,3,2,1],[3,3,2]]=>([(1,5),(2,3),(2,4)],6)=>0
[[5,5,4,3,1],[4,4,3,1]]=>([(2,5),(3,4)],6)=>0
[[3,2,2,2,1],[2,1,1]]=>([(1,4),(2,3),(2,5),(4,5)],6)=>0
[[4,3,3,3,1],[3,2,2,1]]=>([(2,5),(3,4),(4,5)],6)=>0
[[4,3,3,2,1],[3,2,2]]=>([(1,5),(2,3),(2,4)],6)=>0
[[5,4,4,3,1],[4,3,3,1]]=>([(2,5),(3,4)],6)=>0
[[4,3,2,2,1],[3,2,1]]=>([(2,5),(3,4),(3,5)],6)=>0
[[5,4,3,3,1],[4,3,2,1]]=>([(3,5),(4,5)],6)=>0
[[5,4,3,2,1],[4,3,2]]=>([(3,4),(3,5)],6)=>0
[[6,5,4,3,1],[5,4,3,1]]=>([(4,5)],6)=>0
[[2,2,2,2,2],[1,1,1,1]]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>0
[[3,3,3,3,2],[2,2,2,2]]=>([(0,5),(1,3),(4,2),(5,4)],6)=>0
[[3,3,3,2,2],[2,2,2,1]]=>([(0,5),(1,5),(2,3),(3,4)],6)=>0
[[4,4,4,3,2],[3,3,3,2]]=>([(1,3),(2,4),(4,5)],6)=>0
[[3,3,2,2,2],[2,2,1,1]]=>([(0,5),(1,3),(2,4),(4,5)],6)=>0
[[4,4,3,3,2],[3,3,2,2]]=>([(0,5),(1,4),(2,3)],6)=>0
[[4,4,3,2,2],[3,3,2,1]]=>([(1,5),(2,5),(3,4)],6)=>0
[[5,5,4,3,2],[4,4,3,2]]=>([(2,5),(3,4)],6)=>0
[[3,2,2,2,2],[2,1,1,1]]=>([(1,5),(2,3),(3,4),(4,5)],6)=>0
[[4,3,3,3,2],[3,2,2,2]]=>([(1,3),(2,4),(4,5)],6)=>0
[[4,3,3,2,2],[3,2,2,1]]=>([(1,5),(2,5),(3,4)],6)=>0
[[5,4,4,3,2],[4,3,3,2]]=>([(2,5),(3,4)],6)=>0
[[4,3,2,2,2],[3,2,1,1]]=>([(2,5),(3,4),(4,5)],6)=>0
[[5,4,3,3,2],[4,3,2,2]]=>([(2,5),(3,4)],6)=>0
[[5,4,3,2,2],[4,3,2,1]]=>([(3,5),(4,5)],6)=>0
[[6,5,4,3,2],[5,4,3,2]]=>([(4,5)],6)=>0
[[1,1,1,1,1,1],[]]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>0
[[2,2,2,2,2,1],[1,1,1,1,1]]=>([(1,5),(3,4),(4,2),(5,3)],6)=>0
[[2,2,2,2,1,1],[1,1,1,1]]=>([(0,5),(1,3),(4,2),(5,4)],6)=>0
[[3,3,3,3,2,1],[2,2,2,2,1]]=>([(2,3),(3,5),(5,4)],6)=>0
[[2,2,2,1,1,1],[1,1,1]]=>([(0,5),(1,4),(4,2),(5,3)],6)=>0
[[3,3,3,2,2,1],[2,2,2,1,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[3,3,3,2,1,1],[2,2,2,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[4,4,4,3,2,1],[3,3,3,2,1]]=>([(3,4),(4,5)],6)=>0
[[2,2,1,1,1,1],[1,1]]=>([(0,5),(1,3),(4,2),(5,4)],6)=>0
[[3,3,2,2,2,1],[2,2,1,1,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[3,3,2,2,1,1],[2,2,1,1]]=>([(0,5),(1,4),(2,3)],6)=>0
[[4,4,3,3,2,1],[3,3,2,2,1]]=>([(2,5),(3,4)],6)=>0
[[3,3,2,1,1,1],[2,2,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[4,4,3,2,2,1],[3,3,2,1,1]]=>([(2,5),(3,4)],6)=>0
[[4,4,3,2,1,1],[3,3,2,1]]=>([(2,5),(3,4)],6)=>0
[[5,5,4,3,2,1],[4,4,3,2,1]]=>([(4,5)],6)=>0
[[2,1,1,1,1,1],[1]]=>([(1,5),(3,4),(4,2),(5,3)],6)=>0
[[3,2,2,2,2,1],[2,1,1,1,1]]=>([(2,3),(3,5),(5,4)],6)=>0
[[3,2,2,2,1,1],[2,1,1,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[4,3,3,3,2,1],[3,2,2,2,1]]=>([(3,4),(4,5)],6)=>0
[[3,2,2,1,1,1],[2,1,1]]=>([(1,3),(2,4),(4,5)],6)=>0
[[4,3,3,2,2,1],[3,2,2,1,1]]=>([(2,5),(3,4)],6)=>0
[[4,3,3,2,1,1],[3,2,2,1]]=>([(2,5),(3,4)],6)=>0
[[5,4,4,3,2,1],[4,3,3,2,1]]=>([(4,5)],6)=>0
[[3,2,1,1,1,1],[2,1]]=>([(2,3),(3,5),(5,4)],6)=>0
[[4,3,2,2,2,1],[3,2,1,1,1]]=>([(3,4),(4,5)],6)=>0
[[4,3,2,2,1,1],[3,2,1,1]]=>([(2,5),(3,4)],6)=>0
[[5,4,3,3,2,1],[4,3,2,2,1]]=>([(4,5)],6)=>0
[[4,3,2,1,1,1],[3,2,1]]=>([(3,4),(4,5)],6)=>0
[[5,4,3,2,2,1],[4,3,2,1,1]]=>([(4,5)],6)=>0
[[5,4,3,2,1,1],[4,3,2,1]]=>([(4,5)],6)=>0
[[6,5,4,3,2,1],[5,4,3,2,1]]=>([],6)=>0
[[7],[]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>0
[[1,1,1,1,1,1,1],[]]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>0
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Description
The number of simple modules with projective dimension two in the incidence algebra of the poset.
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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