Identifier
- St000073: Gelfand-Tsetlin patterns ⟶ ℤ
Values
=>
Cc0018;cc-rep
[[1]]=>0
[[2]]=>0
[[3]]=>0
[[1,0],[0]]=>0
[[1,0],[1]]=>1
[[2,0],[0]]=>0
[[2,0],[1]]=>0
[[2,0],[2]]=>1
[[1,1],[1]]=>1
[[3,0],[0]]=>0
[[3,0],[1]]=>0
[[3,0],[2]]=>0
[[3,0],[3]]=>1
[[2,1],[1]]=>0
[[2,1],[2]]=>1
[[3,1],[1]]=>0
[[3,1],[2]]=>0
[[3,1],[3]]=>1
[[2,2],[2]]=>1
[[3,2],[2]]=>0
[[3,2],[3]]=>1
[[3,3],[3]]=>1
[[1,0,0],[0,0],[0]]=>2
[[1,0,0],[1,0],[0]]=>2
[[1,0,0],[1,0],[1]]=>3
[[2,0,0],[0,0],[0]]=>2
[[2,0,0],[1,0],[0]]=>1
[[2,0,0],[1,0],[1]]=>2
[[2,0,0],[2,0],[0]]=>2
[[2,0,0],[2,0],[1]]=>2
[[2,0,0],[2,0],[2]]=>3
[[1,1,0],[1,0],[0]]=>1
[[1,1,0],[1,0],[1]]=>2
[[1,1,0],[1,1],[1]]=>3
[[3,0,0],[0,0],[0]]=>2
[[3,0,0],[1,0],[0]]=>1
[[3,0,0],[1,0],[1]]=>2
[[3,0,0],[2,0],[0]]=>1
[[3,0,0],[2,0],[1]]=>1
[[3,0,0],[2,0],[2]]=>2
[[3,0,0],[3,0],[0]]=>2
[[3,0,0],[3,0],[1]]=>2
[[3,0,0],[3,0],[2]]=>2
[[3,0,0],[3,0],[3]]=>3
[[2,1,0],[1,0],[0]]=>0
[[2,1,0],[1,0],[1]]=>1
[[2,1,0],[1,1],[1]]=>2
[[2,1,0],[2,0],[0]]=>1
[[2,1,0],[2,0],[1]]=>1
[[2,1,0],[2,0],[2]]=>2
[[2,1,0],[2,1],[1]]=>2
[[2,1,0],[2,1],[2]]=>3
[[1,1,1],[1,1],[1]]=>3
[[3,1,0],[1,0],[0]]=>0
[[3,1,0],[1,0],[1]]=>1
[[3,1,0],[1,1],[1]]=>2
[[3,1,0],[2,0],[0]]=>0
[[3,1,0],[2,0],[1]]=>0
[[3,1,0],[2,0],[2]]=>1
[[3,1,0],[2,1],[1]]=>1
[[3,1,0],[2,1],[2]]=>2
[[3,1,0],[3,0],[0]]=>1
[[3,1,0],[3,0],[1]]=>1
[[3,1,0],[3,0],[2]]=>1
[[3,1,0],[3,0],[3]]=>2
[[3,1,0],[3,1],[1]]=>2
[[3,1,0],[3,1],[2]]=>2
[[3,1,0],[3,1],[3]]=>3
[[2,2,0],[2,0],[0]]=>1
[[2,2,0],[2,0],[1]]=>1
[[2,2,0],[2,0],[2]]=>2
[[2,2,0],[2,1],[1]]=>1
[[2,2,0],[2,1],[2]]=>2
[[2,2,0],[2,2],[2]]=>3
[[2,1,1],[1,1],[1]]=>2
[[2,1,1],[2,1],[1]]=>2
[[2,1,1],[2,1],[2]]=>3
[[3,2,0],[2,0],[0]]=>0
[[3,2,0],[2,0],[1]]=>0
[[3,2,0],[2,0],[2]]=>1
[[3,2,0],[2,1],[1]]=>0
[[3,2,0],[2,1],[2]]=>1
[[3,2,0],[2,2],[2]]=>2
[[3,2,0],[3,0],[0]]=>1
[[3,2,0],[3,0],[1]]=>1
[[3,2,0],[3,0],[2]]=>1
[[3,2,0],[3,0],[3]]=>2
[[3,2,0],[3,1],[1]]=>1
[[3,2,0],[3,1],[2]]=>1
[[3,2,0],[3,1],[3]]=>2
[[3,2,0],[3,2],[2]]=>2
[[3,2,0],[3,2],[3]]=>3
[[3,1,1],[1,1],[1]]=>2
[[3,1,1],[2,1],[1]]=>1
[[3,1,1],[2,1],[2]]=>2
[[3,1,1],[3,1],[1]]=>2
[[3,1,1],[3,1],[2]]=>2
[[3,1,1],[3,1],[3]]=>3
[[2,2,1],[2,1],[1]]=>1
[[2,2,1],[2,1],[2]]=>2
[[2,2,1],[2,2],[2]]=>3
[[3,3,0],[3,0],[0]]=>1
[[3,3,0],[3,0],[1]]=>1
[[3,3,0],[3,0],[2]]=>1
[[3,3,0],[3,0],[3]]=>2
[[3,3,0],[3,1],[1]]=>1
[[3,3,0],[3,1],[2]]=>1
[[3,3,0],[3,1],[3]]=>2
[[3,3,0],[3,2],[2]]=>1
[[3,3,0],[3,2],[3]]=>2
[[3,3,0],[3,3],[3]]=>3
[[3,2,1],[2,1],[1]]=>0
[[3,2,1],[2,1],[2]]=>1
[[3,2,1],[2,2],[2]]=>2
[[3,2,1],[3,1],[1]]=>1
[[3,2,1],[3,1],[2]]=>1
[[3,2,1],[3,1],[3]]=>2
[[3,2,1],[3,2],[2]]=>2
[[3,2,1],[3,2],[3]]=>3
[[2,2,2],[2,2],[2]]=>3
[[3,3,1],[3,3],[3]]=>3
[[3,3,1],[3,2],[3]]=>2
[[3,3,1],[3,1],[3]]=>2
[[3,3,1],[3,2],[2]]=>1
[[3,3,1],[3,1],[2]]=>1
[[3,3,1],[3,1],[1]]=>1
[[3,2,2],[3,2],[3]]=>3
[[3,2,2],[3,2],[2]]=>2
[[3,2,2],[2,2],[2]]=>2
[[1,0,0,0],[0,0,0],[0,0],[0]]=>5
[[1,0,0,0],[1,0,0],[0,0],[0]]=>5
[[1,0,0,0],[1,0,0],[1,0],[0]]=>5
[[1,0,0,0],[1,0,0],[1,0],[1]]=>6
[[2,0,0,0],[0,0,0],[0,0],[0]]=>5
[[2,0,0,0],[1,0,0],[0,0],[0]]=>4
[[2,0,0,0],[1,0,0],[1,0],[0]]=>4
[[2,0,0,0],[1,0,0],[1,0],[1]]=>5
[[2,0,0,0],[2,0,0],[0,0],[0]]=>5
[[2,0,0,0],[2,0,0],[1,0],[0]]=>4
[[2,0,0,0],[2,0,0],[1,0],[1]]=>5
[[2,0,0,0],[2,0,0],[2,0],[0]]=>5
[[2,0,0,0],[2,0,0],[2,0],[1]]=>5
[[2,0,0,0],[2,0,0],[2,0],[2]]=>6
[[1,1,0,0],[1,0,0],[0,0],[0]]=>4
[[1,1,0,0],[1,0,0],[1,0],[0]]=>4
[[1,1,0,0],[1,0,0],[1,0],[1]]=>5
[[1,1,0,0],[1,1,0],[1,0],[0]]=>4
[[1,1,0,0],[1,1,0],[1,0],[1]]=>5
[[1,1,0,0],[1,1,0],[1,1],[1]]=>6
[[3,0,0,0],[0,0,0],[0,0],[0]]=>5
[[3,0,0,0],[1,0,0],[0,0],[0]]=>4
[[3,0,0,0],[1,0,0],[1,0],[0]]=>4
[[3,0,0,0],[1,0,0],[1,0],[1]]=>5
[[3,0,0,0],[2,0,0],[0,0],[0]]=>4
[[3,0,0,0],[2,0,0],[1,0],[0]]=>3
[[3,0,0,0],[2,0,0],[1,0],[1]]=>4
[[3,0,0,0],[2,0,0],[2,0],[0]]=>4
[[3,0,0,0],[2,0,0],[2,0],[1]]=>4
[[3,0,0,0],[2,0,0],[2,0],[2]]=>5
[[3,0,0,0],[3,0,0],[0,0],[0]]=>5
[[3,0,0,0],[3,0,0],[1,0],[0]]=>4
[[3,0,0,0],[3,0,0],[1,0],[1]]=>5
[[3,0,0,0],[3,0,0],[2,0],[0]]=>4
[[3,0,0,0],[3,0,0],[2,0],[1]]=>4
[[3,0,0,0],[3,0,0],[2,0],[2]]=>5
[[3,0,0,0],[3,0,0],[3,0],[0]]=>5
[[3,0,0,0],[3,0,0],[3,0],[1]]=>5
[[3,0,0,0],[3,0,0],[3,0],[2]]=>5
[[3,0,0,0],[3,0,0],[3,0],[3]]=>6
[[2,1,0,0],[1,0,0],[0,0],[0]]=>3
[[2,1,0,0],[1,0,0],[1,0],[0]]=>3
[[2,1,0,0],[1,0,0],[1,0],[1]]=>4
[[2,1,0,0],[1,1,0],[1,0],[0]]=>3
[[2,1,0,0],[1,1,0],[1,0],[1]]=>4
[[2,1,0,0],[1,1,0],[1,1],[1]]=>5
[[2,1,0,0],[2,0,0],[0,0],[0]]=>4
[[2,1,0,0],[2,0,0],[1,0],[0]]=>3
[[2,1,0,0],[2,0,0],[1,0],[1]]=>4
[[2,1,0,0],[2,0,0],[2,0],[0]]=>4
[[2,1,0,0],[2,0,0],[2,0],[1]]=>4
[[2,1,0,0],[2,0,0],[2,0],[2]]=>5
[[2,1,0,0],[2,1,0],[1,0],[0]]=>3
[[2,1,0,0],[2,1,0],[1,0],[1]]=>4
[[2,1,0,0],[2,1,0],[1,1],[1]]=>5
[[2,1,0,0],[2,1,0],[2,0],[0]]=>4
[[2,1,0,0],[2,1,0],[2,0],[1]]=>4
[[2,1,0,0],[2,1,0],[2,0],[2]]=>5
[[2,1,0,0],[2,1,0],[2,1],[1]]=>5
[[2,1,0,0],[2,1,0],[2,1],[2]]=>6
[[1,1,1,0],[1,1,0],[1,0],[0]]=>3
[[1,1,1,0],[1,1,0],[1,0],[1]]=>4
[[1,1,1,0],[1,1,0],[1,1],[1]]=>5
[[1,1,1,0],[1,1,1],[1,1],[1]]=>6
[[3,1,0,0],[1,0,0],[0,0],[0]]=>3
[[3,1,0,0],[1,0,0],[1,0],[0]]=>3
[[3,1,0,0],[1,0,0],[1,0],[1]]=>4
[[3,1,0,0],[1,1,0],[1,0],[0]]=>3
[[3,1,0,0],[1,1,0],[1,0],[1]]=>4
[[3,1,0,0],[1,1,0],[1,1],[1]]=>5
[[3,1,0,0],[2,0,0],[0,0],[0]]=>3
[[3,1,0,0],[2,0,0],[1,0],[0]]=>2
[[3,1,0,0],[2,0,0],[1,0],[1]]=>3
[[3,1,0,0],[2,0,0],[2,0],[0]]=>3
[[3,1,0,0],[2,0,0],[2,0],[1]]=>3
[[3,1,0,0],[2,0,0],[2,0],[2]]=>4
[[3,1,0,0],[2,1,0],[1,0],[0]]=>2
[[3,1,0,0],[2,1,0],[1,0],[1]]=>3
[[3,1,0,0],[2,1,0],[1,1],[1]]=>4
[[3,1,0,0],[2,1,0],[2,0],[0]]=>3
[[3,1,0,0],[2,1,0],[2,0],[1]]=>3
[[3,1,0,0],[2,1,0],[2,0],[2]]=>4
[[3,1,0,0],[2,1,0],[2,1],[1]]=>4
[[3,1,0,0],[2,1,0],[2,1],[2]]=>5
[[3,1,0,0],[3,0,0],[0,0],[0]]=>4
[[3,1,0,0],[3,0,0],[1,0],[0]]=>3
[[3,1,0,0],[3,0,0],[1,0],[1]]=>4
[[3,1,0,0],[3,0,0],[2,0],[0]]=>3
[[3,1,0,0],[3,0,0],[2,0],[1]]=>3
[[3,1,0,0],[3,0,0],[2,0],[2]]=>4
[[3,1,0,0],[3,0,0],[3,0],[0]]=>4
[[3,1,0,0],[3,0,0],[3,0],[1]]=>4
[[3,1,0,0],[3,0,0],[3,0],[2]]=>4
[[3,1,0,0],[3,0,0],[3,0],[3]]=>5
[[3,1,0,0],[3,1,0],[1,0],[0]]=>3
[[3,1,0,0],[3,1,0],[1,0],[1]]=>4
[[3,1,0,0],[3,1,0],[1,1],[1]]=>5
[[3,1,0,0],[3,1,0],[2,0],[0]]=>3
[[3,1,0,0],[3,1,0],[2,0],[1]]=>3
[[3,1,0,0],[3,1,0],[2,0],[2]]=>4
[[3,1,0,0],[3,1,0],[2,1],[1]]=>4
[[3,1,0,0],[3,1,0],[2,1],[2]]=>5
[[3,1,0,0],[3,1,0],[3,0],[0]]=>4
[[3,1,0,0],[3,1,0],[3,0],[1]]=>4
[[3,1,0,0],[3,1,0],[3,0],[2]]=>4
[[3,1,0,0],[3,1,0],[3,0],[3]]=>5
[[3,1,0,0],[3,1,0],[3,1],[1]]=>5
[[3,1,0,0],[3,1,0],[3,1],[2]]=>5
[[3,1,0,0],[3,1,0],[3,1],[3]]=>6
[[2,2,0,0],[2,0,0],[0,0],[0]]=>4
[[2,2,0,0],[2,0,0],[1,0],[0]]=>3
[[2,2,0,0],[2,0,0],[1,0],[1]]=>4
[[2,2,0,0],[2,0,0],[2,0],[0]]=>4
[[2,2,0,0],[2,0,0],[2,0],[1]]=>4
[[2,2,0,0],[2,0,0],[2,0],[2]]=>5
[[2,2,0,0],[2,1,0],[1,0],[0]]=>2
[[2,2,0,0],[2,1,0],[1,0],[1]]=>3
[[2,2,0,0],[2,1,0],[1,1],[1]]=>4
[[2,2,0,0],[2,1,0],[2,0],[0]]=>3
[[2,2,0,0],[2,1,0],[2,0],[1]]=>3
[[2,2,0,0],[2,1,0],[2,0],[2]]=>4
[[2,2,0,0],[2,1,0],[2,1],[1]]=>4
[[2,2,0,0],[2,1,0],[2,1],[2]]=>5
[[2,2,0,0],[2,2,0],[2,0],[0]]=>4
[[2,2,0,0],[2,2,0],[2,0],[1]]=>4
[[2,2,0,0],[2,2,0],[2,0],[2]]=>5
[[2,2,0,0],[2,2,0],[2,1],[1]]=>4
[[2,2,0,0],[2,2,0],[2,1],[2]]=>5
[[2,2,0,0],[2,2,0],[2,2],[2]]=>6
[[2,1,1,0],[1,1,0],[1,0],[0]]=>2
[[2,1,1,0],[1,1,0],[1,0],[1]]=>3
[[2,1,1,0],[1,1,0],[1,1],[1]]=>4
[[2,1,1,0],[1,1,1],[1,1],[1]]=>5
[[2,1,1,0],[2,1,0],[1,0],[0]]=>2
[[2,1,1,0],[2,1,0],[1,0],[1]]=>3
[[2,1,1,0],[2,1,0],[1,1],[1]]=>4
[[2,1,1,0],[2,1,0],[2,0],[0]]=>3
[[2,1,1,0],[2,1,0],[2,0],[1]]=>3
[[2,1,1,0],[2,1,0],[2,0],[2]]=>4
[[2,1,1,0],[2,1,0],[2,1],[1]]=>4
[[2,1,1,0],[2,1,0],[2,1],[2]]=>5
[[2,1,1,0],[2,1,1],[1,1],[1]]=>5
[[2,1,1,0],[2,1,1],[2,1],[1]]=>5
[[2,1,1,0],[2,1,1],[2,1],[2]]=>6
[[1,1,1,1],[1,1,1],[1,1],[1]]=>6
[[3,2,0,0],[2,0,0],[0,0],[0]]=>3
[[3,2,0,0],[2,0,0],[1,0],[0]]=>2
[[3,2,0,0],[2,0,0],[1,0],[1]]=>3
[[3,2,0,0],[2,0,0],[2,0],[0]]=>3
[[3,2,0,0],[2,0,0],[2,0],[1]]=>3
[[3,2,0,0],[2,0,0],[2,0],[2]]=>4
[[3,2,0,0],[2,1,0],[1,0],[0]]=>1
[[3,2,0,0],[2,1,0],[1,0],[1]]=>2
[[3,2,0,0],[2,1,0],[1,1],[1]]=>3
[[3,2,0,0],[2,1,0],[2,0],[0]]=>2
[[3,2,0,0],[2,1,0],[2,0],[1]]=>2
[[3,2,0,0],[2,1,0],[2,0],[2]]=>3
[[3,2,0,0],[2,1,0],[2,1],[1]]=>3
[[3,2,0,0],[2,1,0],[2,1],[2]]=>4
[[3,2,0,0],[2,2,0],[2,0],[0]]=>3
[[3,2,0,0],[2,2,0],[2,0],[1]]=>3
[[3,2,0,0],[2,2,0],[2,0],[2]]=>4
[[3,2,0,0],[2,2,0],[2,1],[1]]=>3
[[3,2,0,0],[2,2,0],[2,1],[2]]=>4
[[3,2,0,0],[2,2,0],[2,2],[2]]=>5
[[3,2,0,0],[3,0,0],[0,0],[0]]=>4
[[3,2,0,0],[3,0,0],[1,0],[0]]=>3
[[3,2,0,0],[3,0,0],[1,0],[1]]=>4
[[3,2,0,0],[3,0,0],[2,0],[0]]=>3
[[3,2,0,0],[3,0,0],[2,0],[1]]=>3
[[3,2,0,0],[3,0,0],[2,0],[2]]=>4
[[3,2,0,0],[3,0,0],[3,0],[0]]=>4
[[3,2,0,0],[3,0,0],[3,0],[1]]=>4
[[3,2,0,0],[3,0,0],[3,0],[2]]=>4
[[3,2,0,0],[3,0,0],[3,0],[3]]=>5
[[3,2,0,0],[3,1,0],[1,0],[0]]=>2
[[3,2,0,0],[3,1,0],[1,0],[1]]=>3
[[3,2,0,0],[3,1,0],[1,1],[1]]=>4
[[3,2,0,0],[3,1,0],[2,0],[0]]=>2
[[3,2,0,0],[3,1,0],[2,0],[1]]=>2
[[3,2,0,0],[3,1,0],[2,0],[2]]=>3
[[3,2,0,0],[3,1,0],[2,1],[1]]=>3
[[3,2,0,0],[3,1,0],[2,1],[2]]=>4
[[3,2,0,0],[3,1,0],[3,0],[0]]=>3
[[3,2,0,0],[3,1,0],[3,0],[1]]=>3
[[3,2,0,0],[3,1,0],[3,0],[2]]=>3
[[3,2,0,0],[3,1,0],[3,0],[3]]=>4
[[3,2,0,0],[3,1,0],[3,1],[1]]=>4
[[3,2,0,0],[3,1,0],[3,1],[2]]=>4
[[3,2,0,0],[3,1,0],[3,1],[3]]=>5
[[3,2,0,0],[3,2,0],[2,0],[0]]=>3
[[3,2,0,0],[3,2,0],[2,0],[1]]=>3
[[3,2,0,0],[3,2,0],[2,0],[2]]=>4
[[3,2,0,0],[3,2,0],[2,1],[1]]=>3
[[3,2,0,0],[3,2,0],[2,1],[2]]=>4
[[3,2,0,0],[3,2,0],[2,2],[2]]=>5
[[3,2,0,0],[3,2,0],[3,0],[0]]=>4
[[3,2,0,0],[3,2,0],[3,0],[1]]=>4
[[3,2,0,0],[3,2,0],[3,0],[2]]=>4
[[3,2,0,0],[3,2,0],[3,0],[3]]=>5
[[3,2,0,0],[3,2,0],[3,1],[1]]=>4
[[3,2,0,0],[3,2,0],[3,1],[2]]=>4
[[3,2,0,0],[3,2,0],[3,1],[3]]=>5
[[3,2,0,0],[3,2,0],[3,2],[2]]=>5
[[3,2,0,0],[3,2,0],[3,2],[3]]=>6
[[3,1,1,0],[1,1,0],[1,0],[0]]=>2
[[3,1,1,0],[1,1,0],[1,0],[1]]=>3
[[3,1,1,0],[1,1,0],[1,1],[1]]=>4
[[3,1,1,0],[1,1,1],[1,1],[1]]=>5
[[3,1,1,0],[2,1,0],[1,0],[0]]=>1
[[3,1,1,0],[2,1,0],[1,0],[1]]=>2
[[3,1,1,0],[2,1,0],[1,1],[1]]=>3
[[3,1,1,0],[2,1,0],[2,0],[0]]=>2
[[3,1,1,0],[2,1,0],[2,0],[1]]=>2
[[3,1,1,0],[2,1,0],[2,0],[2]]=>3
[[3,1,1,0],[2,1,0],[2,1],[1]]=>3
[[3,1,1,0],[2,1,0],[2,1],[2]]=>4
[[3,1,1,0],[2,1,1],[1,1],[1]]=>4
[[3,1,1,0],[2,1,1],[2,1],[1]]=>4
[[3,1,1,0],[2,1,1],[2,1],[2]]=>5
[[3,1,1,0],[3,1,0],[1,0],[0]]=>2
[[3,1,1,0],[3,1,0],[1,0],[1]]=>3
[[3,1,1,0],[3,1,0],[1,1],[1]]=>4
[[3,1,1,0],[3,1,0],[2,0],[0]]=>2
[[3,1,1,0],[3,1,0],[2,0],[1]]=>2
[[3,1,1,0],[3,1,0],[2,0],[2]]=>3
[[3,1,1,0],[3,1,0],[2,1],[1]]=>3
[[3,1,1,0],[3,1,0],[2,1],[2]]=>4
[[3,1,1,0],[3,1,0],[3,0],[0]]=>3
[[3,1,1,0],[3,1,0],[3,0],[1]]=>3
[[3,1,1,0],[3,1,0],[3,0],[2]]=>3
[[3,1,1,0],[3,1,0],[3,0],[3]]=>4
[[3,1,1,0],[3,1,0],[3,1],[1]]=>4
[[3,1,1,0],[3,1,0],[3,1],[2]]=>4
[[3,1,1,0],[3,1,0],[3,1],[3]]=>5
[[3,1,1,0],[3,1,1],[1,1],[1]]=>5
[[3,1,1,0],[3,1,1],[2,1],[1]]=>4
[[3,1,1,0],[3,1,1],[2,1],[2]]=>5
[[3,1,1,0],[3,1,1],[3,1],[1]]=>5
[[3,1,1,0],[3,1,1],[3,1],[2]]=>5
[[3,1,1,0],[3,1,1],[3,1],[3]]=>6
[[2,2,1,0],[2,1,0],[1,0],[0]]=>1
[[2,2,1,0],[2,1,0],[1,0],[1]]=>2
[[2,2,1,0],[2,1,0],[1,1],[1]]=>3
[[2,2,1,0],[2,1,0],[2,0],[0]]=>2
[[2,2,1,0],[2,1,0],[2,0],[1]]=>2
[[2,2,1,0],[2,1,0],[2,0],[2]]=>3
[[2,2,1,0],[2,1,0],[2,1],[1]]=>3
[[2,2,1,0],[2,1,0],[2,1],[2]]=>4
[[2,2,1,0],[2,1,1],[1,1],[1]]=>4
[[2,2,1,0],[2,1,1],[2,1],[1]]=>4
[[2,2,1,0],[2,1,1],[2,1],[2]]=>5
[[2,2,1,0],[2,2,0],[2,0],[0]]=>3
[[2,2,1,0],[2,2,0],[2,0],[1]]=>3
[[2,2,1,0],[2,2,0],[2,0],[2]]=>4
[[2,2,1,0],[2,2,0],[2,1],[1]]=>3
[[2,2,1,0],[2,2,0],[2,1],[2]]=>4
[[2,2,1,0],[2,2,0],[2,2],[2]]=>5
[[2,2,1,0],[2,2,1],[2,1],[1]]=>4
[[2,2,1,0],[2,2,1],[2,1],[2]]=>5
[[2,2,1,0],[2,2,1],[2,2],[2]]=>6
[[2,1,1,1],[1,1,1],[1,1],[1]]=>5
[[2,1,1,1],[2,1,1],[1,1],[1]]=>5
[[2,1,1,1],[2,1,1],[2,1],[1]]=>5
[[2,1,1,1],[2,1,1],[2,1],[2]]=>6
[[3,3,0,0],[3,2,0],[3,2],[3]]=>5
[[3,3,0,0],[3,2,0],[3,1],[3]]=>4
[[3,3,0,0],[3,1,0],[3,1],[3]]=>5
[[3,3,0,0],[3,2,0],[3,0],[3]]=>4
[[3,3,0,0],[3,1,0],[3,0],[3]]=>4
[[3,3,0,0],[3,0,0],[3,0],[3]]=>5
[[3,3,0,0],[3,2,0],[3,2],[2]]=>4
[[3,3,0,0],[3,2,0],[3,1],[2]]=>3
[[3,3,0,0],[3,2,0],[2,2],[2]]=>4
[[3,3,0,0],[3,1,0],[3,1],[2]]=>4
[[3,3,0,0],[3,2,0],[3,0],[2]]=>3
[[3,3,0,0],[3,2,0],[2,1],[2]]=>3
[[3,3,0,0],[3,1,0],[3,0],[2]]=>3
[[3,3,0,0],[3,1,0],[2,1],[2]]=>4
[[3,3,0,0],[3,0,0],[3,0],[2]]=>4
[[3,3,0,0],[3,2,0],[2,0],[2]]=>3
[[3,3,0,0],[3,1,0],[2,0],[2]]=>3
[[3,3,0,0],[3,0,0],[2,0],[2]]=>4
[[3,3,0,0],[3,2,0],[3,1],[1]]=>3
[[3,3,0,0],[3,1,0],[3,1],[1]]=>4
[[3,3,0,0],[3,2,0],[3,0],[1]]=>3
[[3,3,0,0],[3,2,0],[2,1],[1]]=>2
[[3,3,0,0],[3,1,0],[3,0],[1]]=>3
[[3,3,0,0],[3,1,0],[2,1],[1]]=>3
[[3,3,0,0],[3,0,0],[3,0],[1]]=>4
[[3,3,0,0],[3,2,0],[2,0],[1]]=>2
[[3,3,0,0],[3,1,0],[2,0],[1]]=>2
[[3,3,0,0],[3,1,0],[1,1],[1]]=>4
[[3,3,0,0],[3,0,0],[2,0],[1]]=>3
[[3,3,0,0],[3,1,0],[1,0],[1]]=>3
[[3,3,0,0],[3,0,0],[1,0],[1]]=>4
[[3,3,0,0],[3,2,0],[3,0],[0]]=>3
[[3,3,0,0],[3,1,0],[3,0],[0]]=>3
[[3,3,0,0],[3,0,0],[3,0],[0]]=>4
[[3,3,0,0],[3,2,0],[2,0],[0]]=>2
[[3,3,0,0],[3,1,0],[2,0],[0]]=>2
[[3,3,0,0],[3,0,0],[2,0],[0]]=>3
[[3,3,0,0],[3,1,0],[1,0],[0]]=>2
[[3,3,0,0],[3,0,0],[1,0],[0]]=>3
[[3,3,0,0],[3,0,0],[0,0],[0]]=>4
[[3,2,1,0],[3,2,0],[3,2],[3]]=>5
[[3,2,1,0],[3,2,0],[3,1],[3]]=>4
[[3,2,1,0],[3,1,1],[3,1],[3]]=>5
[[3,2,1,0],[3,1,0],[3,1],[3]]=>4
[[3,2,1,0],[3,2,0],[3,0],[3]]=>4
[[3,2,1,0],[3,1,0],[3,0],[3]]=>3
[[3,2,1,0],[3,2,0],[3,2],[2]]=>4
[[3,2,1,0],[3,2,0],[3,1],[2]]=>3
[[3,2,1,0],[3,1,1],[3,1],[2]]=>4
[[3,2,1,0],[3,2,0],[2,2],[2]]=>4
[[3,2,1,0],[2,2,1],[2,2],[2]]=>5
[[3,2,1,0],[3,1,0],[3,1],[2]]=>3
[[3,2,1,0],[2,2,0],[2,2],[2]]=>4
[[3,2,1,0],[3,2,0],[3,0],[2]]=>3
[[3,2,1,0],[3,2,0],[2,1],[2]]=>3
[[3,2,1,0],[3,1,1],[2,1],[2]]=>4
[[3,2,1,0],[2,2,1],[2,1],[2]]=>4
[[3,2,1,0],[3,1,0],[3,0],[2]]=>2
[[3,2,1,0],[3,1,0],[2,1],[2]]=>3
[[3,2,1,0],[2,2,0],[2,1],[2]]=>3
[[3,2,1,0],[2,1,1],[2,1],[2]]=>4
[[3,2,1,0],[2,1,0],[2,1],[2]]=>3
[[3,2,1,0],[3,2,0],[2,0],[2]]=>3
[[3,2,1,0],[3,1,0],[2,0],[2]]=>2
[[3,2,1,0],[2,2,0],[2,0],[2]]=>3
[[3,2,1,0],[2,1,0],[2,0],[2]]=>2
[[3,2,1,0],[3,2,0],[3,1],[1]]=>3
[[3,2,1,0],[3,1,1],[3,1],[1]]=>4
[[3,2,1,0],[3,1,0],[3,1],[1]]=>3
[[3,2,1,0],[3,2,0],[3,0],[1]]=>3
[[3,2,1,0],[3,2,0],[2,1],[1]]=>2
[[3,2,1,0],[3,1,1],[2,1],[1]]=>3
[[3,2,1,0],[2,2,1],[2,1],[1]]=>3
[[3,2,1,0],[3,1,0],[3,0],[1]]=>2
[[3,2,1,0],[3,1,0],[2,1],[1]]=>2
[[3,2,1,0],[2,2,0],[2,1],[1]]=>2
[[3,2,1,0],[2,1,1],[2,1],[1]]=>3
[[3,2,1,0],[2,1,0],[2,1],[1]]=>2
[[3,2,1,0],[3,2,0],[2,0],[1]]=>2
[[3,2,1,0],[3,1,1],[1,1],[1]]=>4
[[3,2,1,0],[3,1,0],[2,0],[1]]=>1
[[3,2,1,0],[2,2,0],[2,0],[1]]=>2
[[3,2,1,0],[3,1,0],[1,1],[1]]=>3
[[3,2,1,0],[2,1,1],[1,1],[1]]=>3
[[3,2,1,0],[2,1,0],[2,0],[1]]=>1
[[3,2,1,0],[2,1,0],[1,1],[1]]=>2
[[3,2,1,0],[3,1,0],[1,0],[1]]=>2
[[3,2,1,0],[2,1,0],[1,0],[1]]=>1
[[3,2,1,0],[3,2,0],[3,0],[0]]=>3
[[3,2,1,0],[3,1,0],[3,0],[0]]=>2
[[3,2,1,0],[3,2,0],[2,0],[0]]=>2
[[3,2,1,0],[3,1,0],[2,0],[0]]=>1
[[3,2,1,0],[2,2,0],[2,0],[0]]=>2
[[3,2,1,0],[2,1,0],[2,0],[0]]=>1
[[3,2,1,0],[3,1,0],[1,0],[0]]=>1
[[3,2,1,0],[2,1,0],[1,0],[0]]=>0
[[3,1,1,1],[3,1,1],[3,1],[3]]=>6
[[3,1,1,1],[3,1,1],[3,1],[2]]=>5
[[3,1,1,1],[3,1,1],[2,1],[2]]=>5
[[3,1,1,1],[2,1,1],[2,1],[2]]=>5
[[3,1,1,1],[3,1,1],[3,1],[1]]=>5
[[3,1,1,1],[3,1,1],[2,1],[1]]=>4
[[3,1,1,1],[2,1,1],[2,1],[1]]=>4
[[3,1,1,1],[3,1,1],[1,1],[1]]=>5
[[3,1,1,1],[2,1,1],[1,1],[1]]=>4
[[3,1,1,1],[1,1,1],[1,1],[1]]=>5
[[2,2,2,0],[2,2,1],[2,2],[2]]=>5
[[2,2,2,0],[2,2,0],[2,2],[2]]=>5
[[2,2,2,0],[2,2,1],[2,1],[2]]=>4
[[2,2,2,0],[2,2,0],[2,1],[2]]=>4
[[2,2,2,0],[2,2,0],[2,0],[2]]=>4
[[2,2,2,0],[2,2,1],[2,1],[1]]=>3
[[2,2,2,0],[2,2,0],[2,1],[1]]=>3
[[2,2,2,0],[2,2,0],[2,0],[1]]=>3
[[2,2,2,0],[2,2,0],[2,0],[0]]=>3
[[2,2,1,1],[2,2,1],[2,2],[2]]=>6
[[2,2,1,1],[2,2,1],[2,1],[2]]=>5
[[2,2,1,1],[2,1,1],[2,1],[2]]=>5
[[2,2,1,1],[2,2,1],[2,1],[1]]=>4
[[2,2,1,1],[2,1,1],[2,1],[1]]=>4
[[2,2,1,1],[2,1,1],[1,1],[1]]=>4
[]=>0
[[0]]=>0
[[0,0],[0]]=>1
[[0,0,0],[0,0],[0]]=>3
[[3,3,2],[3,2],[2]]=>1
[[3,3,2],[3,2],[3]]=>2
[[3,3,2],[3,3],[3]]=>3
[[3,3,3],[3,3],[3]]=>3
[[0,0,0,0],[0,0,0],[0,0],[0]]=>6
[[2,2,2,0],[2,2,2],[2,2],[2]]=>6
[[2,2,2,1],[2,2,1],[2,1],[1]]=>3
[[2,2,2,1],[2,2,1],[2,1],[2]]=>4
[[2,2,2,1],[2,2,1],[2,2],[2]]=>5
[[2,2,2,1],[2,2,2],[2,2],[2]]=>6
[[2,2,2,2],[2,2,2],[2,2],[2]]=>6
[[3,2,1,0],[3,2,1],[2,1],[1]]=>3
[[3,2,1,0],[3,2,1],[2,1],[2]]=>4
[[3,2,1,0],[3,2,1],[2,2],[2]]=>5
[[3,2,1,0],[3,2,1],[3,1],[1]]=>4
[[3,2,1,0],[3,2,1],[3,1],[2]]=>4
[[3,2,1,0],[3,2,1],[3,1],[3]]=>5
[[3,2,1,0],[3,2,1],[3,2],[2]]=>5
[[3,2,1,0],[3,2,1],[3,2],[3]]=>6
[[3,2,1,1],[2,1,1],[1,1],[1]]=>3
[[3,2,1,1],[2,1,1],[2,1],[1]]=>3
[[3,2,1,1],[2,1,1],[2,1],[2]]=>4
[[3,2,1,1],[2,2,1],[2,1],[1]]=>3
[[3,2,1,1],[2,2,1],[2,1],[2]]=>4
[[3,2,1,1],[2,2,1],[2,2],[2]]=>5
[[3,2,1,1],[3,1,1],[1,1],[1]]=>4
[[3,2,1,1],[3,1,1],[2,1],[1]]=>3
[[3,2,1,1],[3,1,1],[2,1],[2]]=>4
[[3,2,1,1],[3,1,1],[3,1],[1]]=>4
[[3,2,1,1],[3,1,1],[3,1],[2]]=>4
[[3,2,1,1],[3,1,1],[3,1],[3]]=>5
[[3,2,1,1],[3,2,1],[2,1],[1]]=>3
[[3,2,1,1],[3,2,1],[2,1],[2]]=>4
[[3,2,1,1],[3,2,1],[2,2],[2]]=>5
[[3,2,1,1],[3,2,1],[3,1],[1]]=>4
[[3,2,1,1],[3,2,1],[3,1],[2]]=>4
[[3,2,1,1],[3,2,1],[3,1],[3]]=>5
[[3,2,1,1],[3,2,1],[3,2],[2]]=>5
[[3,2,1,1],[3,2,1],[3,2],[3]]=>6
[[3,2,2,0],[2,2,0],[2,0],[0]]=>2
[[3,2,2,0],[2,2,0],[2,0],[1]]=>2
[[3,2,2,0],[2,2,0],[2,0],[2]]=>3
[[3,2,2,0],[2,2,0],[2,1],[1]]=>2
[[3,2,2,0],[2,2,0],[2,1],[2]]=>3
[[3,2,2,0],[2,2,0],[2,2],[2]]=>4
[[3,2,2,0],[2,2,1],[2,1],[1]]=>2
[[3,2,2,0],[2,2,1],[2,1],[2]]=>3
[[3,2,2,0],[2,2,1],[2,2],[2]]=>4
[[3,2,2,0],[2,2,2],[2,2],[2]]=>5
[[3,2,2,0],[3,2,0],[2,0],[0]]=>2
[[3,2,2,0],[3,2,0],[2,0],[1]]=>2
[[3,2,2,0],[3,2,0],[2,0],[2]]=>3
[[3,2,2,0],[3,2,0],[2,1],[1]]=>2
[[3,2,2,0],[3,2,0],[2,1],[2]]=>3
[[3,2,2,0],[3,2,0],[2,2],[2]]=>4
[[3,2,2,0],[3,2,0],[3,0],[0]]=>3
[[3,2,2,0],[3,2,0],[3,0],[1]]=>3
[[3,2,2,0],[3,2,0],[3,0],[2]]=>3
[[3,2,2,0],[3,2,0],[3,0],[3]]=>4
[[3,2,2,0],[3,2,0],[3,1],[1]]=>3
[[3,2,2,0],[3,2,0],[3,1],[2]]=>3
[[3,2,2,0],[3,2,0],[3,1],[3]]=>4
[[3,2,2,0],[3,2,0],[3,2],[2]]=>4
[[3,2,2,0],[3,2,0],[3,2],[3]]=>5
[[3,2,2,0],[3,2,1],[2,1],[1]]=>2
[[3,2,2,0],[3,2,1],[2,1],[2]]=>3
[[3,2,2,0],[3,2,1],[2,2],[2]]=>4
[[3,2,2,0],[3,2,1],[3,1],[1]]=>3
[[3,2,2,0],[3,2,1],[3,1],[2]]=>3
[[3,2,2,0],[3,2,1],[3,1],[3]]=>4
[[3,2,2,0],[3,2,1],[3,2],[2]]=>4
[[3,2,2,0],[3,2,1],[3,2],[3]]=>5
[[3,2,2,0],[3,2,2],[2,2],[2]]=>5
[[3,2,2,0],[3,2,2],[3,2],[2]]=>5
[[3,2,2,0],[3,2,2],[3,2],[3]]=>6
[[3,2,2,1],[2,2,1],[2,1],[1]]=>2
[[3,2,2,1],[2,2,1],[2,1],[2]]=>3
[[3,2,2,1],[2,2,1],[2,2],[2]]=>4
[[3,2,2,1],[2,2,2],[2,2],[2]]=>5
[[3,2,2,1],[3,2,1],[2,1],[1]]=>2
[[3,2,2,1],[3,2,1],[2,1],[2]]=>3
[[3,2,2,1],[3,2,1],[2,2],[2]]=>4
[[3,2,2,1],[3,2,1],[3,1],[1]]=>3
[[3,2,2,1],[3,2,1],[3,1],[2]]=>3
[[3,2,2,1],[3,2,1],[3,1],[3]]=>4
[[3,2,2,1],[3,2,1],[3,2],[2]]=>4
[[3,2,2,1],[3,2,1],[3,2],[3]]=>5
[[3,2,2,1],[3,2,2],[2,2],[2]]=>5
[[3,2,2,1],[3,2,2],[3,2],[2]]=>5
[[3,2,2,1],[3,2,2],[3,2],[3]]=>6
[[3,2,2,2],[2,2,2],[2,2],[2]]=>5
[[3,2,2,2],[3,2,2],[2,2],[2]]=>5
[[3,2,2,2],[3,2,2],[3,2],[2]]=>5
[[3,2,2,2],[3,2,2],[3,2],[3]]=>6
[[3,3,0,0],[3,3,0],[3,0],[0]]=>4
[[3,3,0,0],[3,3,0],[3,0],[1]]=>4
[[3,3,0,0],[3,3,0],[3,0],[2]]=>4
[[3,3,0,0],[3,3,0],[3,0],[3]]=>5
[[3,3,0,0],[3,3,0],[3,1],[1]]=>4
[[3,3,0,0],[3,3,0],[3,1],[2]]=>4
[[3,3,0,0],[3,3,0],[3,1],[3]]=>5
[[3,3,0,0],[3,3,0],[3,2],[2]]=>4
[[3,3,0,0],[3,3,0],[3,2],[3]]=>5
[[3,3,0,0],[3,3,0],[3,3],[3]]=>6
[[3,3,1,0],[3,1,0],[1,0],[0]]=>1
[[3,3,1,0],[3,1,0],[1,0],[1]]=>2
[[3,3,1,0],[3,1,0],[1,1],[1]]=>3
[[3,3,1,0],[3,1,0],[2,0],[0]]=>1
[[3,3,1,0],[3,1,0],[2,0],[1]]=>1
[[3,3,1,0],[3,1,0],[2,0],[2]]=>2
[[3,3,1,0],[3,1,0],[2,1],[1]]=>2
[[3,3,1,0],[3,1,0],[2,1],[2]]=>3
[[3,3,1,0],[3,1,0],[3,0],[0]]=>2
[[3,3,1,0],[3,1,0],[3,0],[1]]=>2
[[3,3,1,0],[3,1,0],[3,0],[2]]=>2
[[3,3,1,0],[3,1,0],[3,0],[3]]=>3
[[3,3,1,0],[3,1,0],[3,1],[1]]=>3
[[3,3,1,0],[3,1,0],[3,1],[2]]=>3
[[3,3,1,0],[3,1,0],[3,1],[3]]=>4
[[3,3,1,0],[3,1,1],[1,1],[1]]=>4
[[3,3,1,0],[3,1,1],[2,1],[1]]=>3
[[3,3,1,0],[3,1,1],[2,1],[2]]=>4
[[3,3,1,0],[3,1,1],[3,1],[1]]=>4
[[3,3,1,0],[3,1,1],[3,1],[2]]=>4
[[3,3,1,0],[3,1,1],[3,1],[3]]=>5
[[3,3,1,0],[3,2,0],[2,0],[0]]=>1
[[3,3,1,0],[3,2,0],[2,0],[1]]=>1
[[3,3,1,0],[3,2,0],[2,0],[2]]=>2
[[3,3,1,0],[3,2,0],[2,1],[1]]=>1
[[3,3,1,0],[3,2,0],[2,1],[2]]=>2
[[3,3,1,0],[3,2,0],[2,2],[2]]=>3
[[3,3,1,0],[3,2,0],[3,0],[0]]=>2
[[3,3,1,0],[3,2,0],[3,0],[1]]=>2
[[3,3,1,0],[3,2,0],[3,0],[2]]=>2
[[3,3,1,0],[3,2,0],[3,0],[3]]=>3
[[3,3,1,0],[3,2,0],[3,1],[1]]=>2
[[3,3,1,0],[3,2,0],[3,1],[2]]=>2
[[3,3,1,0],[3,2,0],[3,1],[3]]=>3
[[3,3,1,0],[3,2,0],[3,2],[2]]=>3
[[3,3,1,0],[3,2,0],[3,2],[3]]=>4
[[3,3,1,0],[3,2,1],[2,1],[1]]=>2
[[3,3,1,0],[3,2,1],[2,1],[2]]=>3
[[3,3,1,0],[3,2,1],[2,2],[2]]=>4
[[3,3,1,0],[3,2,1],[3,1],[1]]=>3
[[3,3,1,0],[3,2,1],[3,1],[2]]=>3
[[3,3,1,0],[3,2,1],[3,1],[3]]=>4
[[3,3,1,0],[3,2,1],[3,2],[2]]=>4
[[3,3,1,0],[3,2,1],[3,2],[3]]=>5
[[3,3,1,0],[3,3,0],[3,0],[0]]=>3
[[3,3,1,0],[3,3,0],[3,0],[1]]=>3
[[3,3,1,0],[3,3,0],[3,0],[2]]=>3
[[3,3,1,0],[3,3,0],[3,0],[3]]=>4
[[3,3,1,0],[3,3,0],[3,1],[1]]=>3
[[3,3,1,0],[3,3,0],[3,1],[2]]=>3
[[3,3,1,0],[3,3,0],[3,1],[3]]=>4
[[3,3,1,0],[3,3,0],[3,2],[2]]=>3
[[3,3,1,0],[3,3,0],[3,2],[3]]=>4
[[3,3,1,0],[3,3,0],[3,3],[3]]=>5
[[3,3,1,0],[3,3,1],[3,1],[1]]=>4
[[3,3,1,0],[3,3,1],[3,1],[2]]=>4
[[3,3,1,0],[3,3,1],[3,1],[3]]=>5
[[3,3,1,0],[3,3,1],[3,2],[2]]=>4
[[3,3,1,0],[3,3,1],[3,2],[3]]=>5
[[3,3,1,0],[3,3,1],[3,3],[3]]=>6
[[3,3,1,1],[3,1,1],[1,1],[1]]=>4
[[3,3,1,1],[3,1,1],[2,1],[1]]=>3
[[3,3,1,1],[3,1,1],[2,1],[2]]=>4
[[3,3,1,1],[3,1,1],[3,1],[1]]=>4
[[3,3,1,1],[3,1,1],[3,1],[2]]=>4
[[3,3,1,1],[3,1,1],[3,1],[3]]=>5
[[3,3,1,1],[3,2,1],[2,1],[1]]=>2
[[3,3,1,1],[3,2,1],[2,1],[2]]=>3
[[3,3,1,1],[3,2,1],[2,2],[2]]=>4
[[3,3,1,1],[3,2,1],[3,1],[1]]=>3
[[3,3,1,1],[3,2,1],[3,1],[2]]=>3
[[3,3,1,1],[3,2,1],[3,1],[3]]=>4
[[3,3,1,1],[3,2,1],[3,2],[2]]=>4
[[3,3,1,1],[3,2,1],[3,2],[3]]=>5
[[3,3,1,1],[3,3,1],[3,1],[1]]=>4
[[3,3,1,1],[3,3,1],[3,1],[2]]=>4
[[3,3,1,1],[3,3,1],[3,1],[3]]=>5
[[3,3,1,1],[3,3,1],[3,2],[2]]=>4
[[3,3,1,1],[3,3,1],[3,2],[3]]=>5
[[3,3,1,1],[3,3,1],[3,3],[3]]=>6
[[3,3,2,0],[3,2,0],[2,0],[0]]=>1
[[3,3,2,0],[3,2,0],[2,0],[1]]=>1
[[3,3,2,0],[3,2,0],[2,0],[2]]=>2
[[3,3,2,0],[3,2,0],[2,1],[1]]=>1
[[3,3,2,0],[3,2,0],[2,1],[2]]=>2
[[3,3,2,0],[3,2,0],[2,2],[2]]=>3
[[3,3,2,0],[3,2,0],[3,0],[0]]=>2
[[3,3,2,0],[3,2,0],[3,0],[1]]=>2
[[3,3,2,0],[3,2,0],[3,0],[2]]=>2
[[3,3,2,0],[3,2,0],[3,0],[3]]=>3
[[3,3,2,0],[3,2,0],[3,1],[1]]=>2
[[3,3,2,0],[3,2,0],[3,1],[2]]=>2
[[3,3,2,0],[3,2,0],[3,1],[3]]=>3
[[3,3,2,0],[3,2,0],[3,2],[2]]=>3
[[3,3,2,0],[3,2,0],[3,2],[3]]=>4
[[3,3,2,0],[3,2,1],[2,1],[1]]=>1
[[3,3,2,0],[3,2,1],[2,1],[2]]=>2
[[3,3,2,0],[3,2,1],[2,2],[2]]=>3
[[3,3,2,0],[3,2,1],[3,1],[1]]=>2
[[3,3,2,0],[3,2,1],[3,1],[2]]=>2
[[3,3,2,0],[3,2,1],[3,1],[3]]=>3
[[3,3,2,0],[3,2,1],[3,2],[2]]=>3
[[3,3,2,0],[3,2,1],[3,2],[3]]=>4
[[3,3,2,0],[3,2,2],[2,2],[2]]=>4
[[3,3,2,0],[3,2,2],[3,2],[2]]=>4
[[3,3,2,0],[3,2,2],[3,2],[3]]=>5
[[3,3,2,0],[3,3,0],[3,0],[0]]=>3
[[3,3,2,0],[3,3,0],[3,0],[1]]=>3
[[3,3,2,0],[3,3,0],[3,0],[2]]=>3
[[3,3,2,0],[3,3,0],[3,0],[3]]=>4
[[3,3,2,0],[3,3,0],[3,1],[1]]=>3
[[3,3,2,0],[3,3,0],[3,1],[2]]=>3
[[3,3,2,0],[3,3,0],[3,1],[3]]=>4
[[3,3,2,0],[3,3,0],[3,2],[2]]=>3
[[3,3,2,0],[3,3,0],[3,2],[3]]=>4
[[3,3,2,0],[3,3,0],[3,3],[3]]=>5
[[3,3,2,0],[3,3,1],[3,1],[1]]=>3
[[3,3,2,0],[3,3,1],[3,1],[2]]=>3
[[3,3,2,0],[3,3,1],[3,1],[3]]=>4
[[3,3,2,0],[3,3,1],[3,2],[2]]=>3
[[3,3,2,0],[3,3,1],[3,2],[3]]=>4
[[3,3,2,0],[3,3,1],[3,3],[3]]=>5
[[3,3,2,0],[3,3,2],[3,2],[2]]=>4
[[3,3,2,0],[3,3,2],[3,2],[3]]=>5
[[3,3,2,0],[3,3,2],[3,3],[3]]=>6
[[3,3,2,1],[3,2,1],[2,1],[1]]=>1
[[3,3,2,1],[3,2,1],[2,1],[2]]=>2
[[3,3,2,1],[3,2,1],[2,2],[2]]=>3
[[3,3,2,1],[3,2,1],[3,1],[1]]=>2
[[3,3,2,1],[3,2,1],[3,1],[2]]=>2
[[3,3,2,1],[3,2,1],[3,1],[3]]=>3
[[3,3,2,1],[3,2,1],[3,2],[2]]=>3
[[3,3,2,1],[3,2,1],[3,2],[3]]=>4
[[3,3,2,1],[3,2,2],[2,2],[2]]=>4
[[3,3,2,1],[3,2,2],[3,2],[2]]=>4
[[3,3,2,1],[3,2,2],[3,2],[3]]=>5
[[3,3,2,1],[3,3,1],[3,1],[1]]=>3
[[3,3,2,1],[3,3,1],[3,1],[2]]=>3
[[3,3,2,1],[3,3,1],[3,1],[3]]=>4
[[3,3,2,1],[3,3,1],[3,2],[2]]=>3
[[3,3,2,1],[3,3,1],[3,2],[3]]=>4
[[3,3,2,1],[3,3,1],[3,3],[3]]=>5
[[3,3,2,1],[3,3,2],[3,2],[2]]=>4
[[3,3,2,1],[3,3,2],[3,2],[3]]=>5
[[3,3,2,1],[3,3,2],[3,3],[3]]=>6
[[3,3,2,2],[3,2,2],[2,2],[2]]=>4
[[3,3,2,2],[3,2,2],[3,2],[2]]=>4
[[3,3,2,2],[3,2,2],[3,2],[3]]=>5
[[3,3,2,2],[3,3,2],[3,2],[2]]=>4
[[3,3,2,2],[3,3,2],[3,2],[3]]=>5
[[3,3,2,2],[3,3,2],[3,3],[3]]=>6
[[3,3,3,0],[3,3,0],[3,0],[0]]=>3
[[3,3,3,0],[3,3,0],[3,0],[1]]=>3
[[3,3,3,0],[3,3,0],[3,0],[2]]=>3
[[3,3,3,0],[3,3,0],[3,0],[3]]=>4
[[3,3,3,0],[3,3,0],[3,1],[1]]=>3
[[3,3,3,0],[3,3,0],[3,1],[2]]=>3
[[3,3,3,0],[3,3,0],[3,1],[3]]=>4
[[3,3,3,0],[3,3,0],[3,2],[2]]=>3
[[3,3,3,0],[3,3,0],[3,2],[3]]=>4
[[3,3,3,0],[3,3,0],[3,3],[3]]=>5
[[3,3,3,0],[3,3,1],[3,1],[1]]=>3
[[3,3,3,0],[3,3,1],[3,1],[2]]=>3
[[3,3,3,0],[3,3,1],[3,1],[3]]=>4
[[3,3,3,0],[3,3,1],[3,2],[2]]=>3
[[3,3,3,0],[3,3,1],[3,2],[3]]=>4
[[3,3,3,0],[3,3,1],[3,3],[3]]=>5
[[3,3,3,0],[3,3,2],[3,2],[2]]=>3
[[3,3,3,0],[3,3,2],[3,2],[3]]=>4
[[3,3,3,0],[3,3,2],[3,3],[3]]=>5
[[3,3,3,0],[3,3,3],[3,3],[3]]=>6
[[3,3,3,1],[3,3,1],[3,1],[1]]=>3
[[3,3,3,1],[3,3,1],[3,1],[2]]=>3
[[3,3,3,1],[3,3,1],[3,1],[3]]=>4
[[3,3,3,1],[3,3,1],[3,2],[2]]=>3
[[3,3,3,1],[3,3,1],[3,2],[3]]=>4
[[3,3,3,1],[3,3,1],[3,3],[3]]=>5
[[3,3,3,1],[3,3,2],[3,2],[2]]=>3
[[3,3,3,1],[3,3,2],[3,2],[3]]=>4
[[3,3,3,1],[3,3,2],[3,3],[3]]=>5
[[3,3,3,1],[3,3,3],[3,3],[3]]=>6
[[3,3,3,2],[3,3,2],[3,2],[2]]=>3
[[3,3,3,2],[3,3,2],[3,2],[3]]=>4
[[3,3,3,2],[3,3,2],[3,3],[3]]=>5
[[3,3,3,2],[3,3,3],[3,3],[3]]=>6
[[3,3,3,3],[3,3,3],[3,3],[3]]=>6
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Description
The number of boxed entries.
An entry of a Gelfand-Tsetlin pattern is boxed if $a_{i,j} = a_{i-1,j-1}$ (the northwest neighbor is the same).
An entry of a Gelfand-Tsetlin pattern is boxed if $a_{i,j} = a_{i-1,j-1}$ (the northwest neighbor is the same).
References
[1] Brubaker, B., Bump, D., Friedberg, S. Weyl group multiple Dirichlet series: type A combinatorial theory MathSciNet:2791904
Code
def statistic(g): return g.number_of_boxes()
Created
Jun 11, 2013 at 14:22 by Travis Scrimshaw
Updated
May 29, 2015 at 16:27 by Martin Rubey
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