Identifier
- St000173: Semistandard tableaux ⟶ ℤ
Values
=>
Cc0019;cc-rep
[[1]]=>0
[[2]]=>1
[[3]]=>1
[[4]]=>1
[[1,1]]=>0
[[1,2]]=>1
[[2,2]]=>1
[[1],[2]]=>0
[[1,3]]=>1
[[2,3]]=>2
[[3,3]]=>1
[[1],[3]]=>1
[[2],[3]]=>2
[[1,4]]=>1
[[2,4]]=>2
[[3,4]]=>2
[[4,4]]=>1
[[1],[4]]=>1
[[2],[4]]=>2
[[3],[4]]=>2
[[1,1,1]]=>0
[[1,1,2]]=>1
[[1,2,2]]=>1
[[2,2,2]]=>1
[[1,1],[2]]=>0
[[1,2],[2]]=>1
[[1,1,3]]=>1
[[1,2,3]]=>2
[[1,3,3]]=>1
[[2,2,3]]=>2
[[2,3,3]]=>2
[[3,3,3]]=>1
[[1,1],[3]]=>1
[[1,2],[3]]=>2
[[1,3],[2]]=>1
[[1,3],[3]]=>2
[[2,2],[3]]=>2
[[2,3],[3]]=>3
[[1],[2],[3]]=>0
[[1,1,4]]=>1
[[1,2,4]]=>2
[[1,3,4]]=>2
[[1,4,4]]=>1
[[2,2,4]]=>2
[[2,3,4]]=>3
[[2,4,4]]=>2
[[3,3,4]]=>2
[[3,4,4]]=>2
[[4,4,4]]=>1
[[1,1],[4]]=>1
[[1,2],[4]]=>2
[[1,4],[2]]=>1
[[1,3],[4]]=>2
[[1,4],[3]]=>2
[[1,4],[4]]=>2
[[2,2],[4]]=>2
[[2,3],[4]]=>3
[[2,4],[3]]=>3
[[2,4],[4]]=>3
[[3,3],[4]]=>2
[[3,4],[4]]=>3
[[1],[2],[4]]=>1
[[1],[3],[4]]=>2
[[2],[3],[4]]=>3
[[1,1,1,1]]=>0
[[1,1,1,2]]=>1
[[1,1,2,2]]=>1
[[1,2,2,2]]=>1
[[2,2,2,2]]=>1
[[1,1,1],[2]]=>0
[[1,1,2],[2]]=>1
[[1,2,2],[2]]=>1
[[1,1],[2,2]]=>0
[[1,1,1,3]]=>1
[[1,1,2,3]]=>2
[[1,1,3,3]]=>1
[[1,2,2,3]]=>2
[[1,2,3,3]]=>2
[[1,3,3,3]]=>1
[[2,2,2,3]]=>2
[[2,2,3,3]]=>2
[[2,3,3,3]]=>2
[[3,3,3,3]]=>1
[[1,1,1],[3]]=>1
[[1,1,2],[3]]=>2
[[1,1,3],[2]]=>1
[[1,1,3],[3]]=>2
[[1,2,2],[3]]=>2
[[1,2,3],[2]]=>2
[[1,2,3],[3]]=>3
[[1,3,3],[2]]=>1
[[1,3,3],[3]]=>2
[[2,2,2],[3]]=>2
[[2,2,3],[3]]=>3
[[2,3,3],[3]]=>3
[[1,1],[2,3]]=>1
[[1,1],[3,3]]=>1
[[1,2],[2,3]]=>2
[[1,2],[3,3]]=>2
[[2,2],[3,3]]=>2
[[1,1],[2],[3]]=>0
[[1,2],[2],[3]]=>1
[[1,3],[2],[3]]=>1
[[1,1,1,4]]=>1
[[1,1,2,4]]=>2
[[1,1,3,4]]=>2
[[1,1,4,4]]=>1
[[1,2,2,4]]=>2
[[1,2,3,4]]=>3
[[1,2,4,4]]=>2
[[1,3,3,4]]=>2
[[1,3,4,4]]=>2
[[1,4,4,4]]=>1
[[2,2,2,4]]=>2
[[2,2,3,4]]=>3
[[2,2,4,4]]=>2
[[2,3,3,4]]=>3
[[2,3,4,4]]=>3
[[2,4,4,4]]=>2
[[3,3,3,4]]=>2
[[3,3,4,4]]=>2
[[3,4,4,4]]=>2
[[4,4,4,4]]=>1
[[1,1,1],[4]]=>1
[[1,1,2],[4]]=>2
[[1,1,4],[2]]=>1
[[1,1,3],[4]]=>2
[[1,1,4],[3]]=>2
[[1,1,4],[4]]=>2
[[1,2,2],[4]]=>2
[[1,2,4],[2]]=>2
[[1,2,3],[4]]=>3
[[1,2,4],[3]]=>3
[[1,3,4],[2]]=>2
[[1,2,4],[4]]=>3
[[1,4,4],[2]]=>1
[[1,3,3],[4]]=>2
[[1,3,4],[3]]=>3
[[1,3,4],[4]]=>3
[[1,4,4],[3]]=>2
[[1,4,4],[4]]=>2
[[2,2,2],[4]]=>2
[[2,2,3],[4]]=>3
[[2,2,4],[3]]=>3
[[2,2,4],[4]]=>3
[[2,3,3],[4]]=>3
[[2,3,4],[3]]=>4
[[2,3,4],[4]]=>4
[[2,4,4],[3]]=>3
[[2,4,4],[4]]=>3
[[3,3,3],[4]]=>2
[[3,3,4],[4]]=>3
[[3,4,4],[4]]=>3
[[1,1],[2,4]]=>1
[[1,1],[3,4]]=>2
[[1,1],[4,4]]=>1
[[1,2],[2,4]]=>2
[[1,2],[3,4]]=>3
[[1,3],[2,4]]=>2
[[1,2],[4,4]]=>2
[[1,3],[3,4]]=>3
[[1,3],[4,4]]=>2
[[2,2],[3,4]]=>3
[[2,2],[4,4]]=>2
[[2,3],[3,4]]=>4
[[2,3],[4,4]]=>3
[[3,3],[4,4]]=>2
[[1,1],[2],[4]]=>1
[[1,1],[3],[4]]=>2
[[1,2],[2],[4]]=>2
[[1,2],[3],[4]]=>3
[[1,3],[2],[4]]=>2
[[1,4],[2],[3]]=>1
[[1,4],[2],[4]]=>2
[[1,3],[3],[4]]=>3
[[1,4],[3],[4]]=>3
[[2,2],[3],[4]]=>3
[[2,3],[3],[4]]=>4
[[2,4],[3],[4]]=>4
[[1],[2],[3],[4]]=>0
[[1,1,1,1,1]]=>0
[[1,1,1,1,2]]=>1
[[1,1,1,2,2]]=>1
[[1,1,2,2,2]]=>1
[[1,2,2,2,2]]=>1
[[2,2,2,2,2]]=>1
[[1,1,1,1],[2]]=>0
[[1,1,1,2],[2]]=>1
[[1,1,2,2],[2]]=>1
[[1,2,2,2],[2]]=>1
[[1,1,1],[2,2]]=>0
[[1,1,2],[2,2]]=>1
[[1,1,1,1,3]]=>1
[[1,1,1,2,3]]=>2
[[1,1,1,3,3]]=>1
[[1,1,2,2,3]]=>2
[[1,1,2,3,3]]=>2
[[1,1,3,3,3]]=>1
[[1,2,2,2,3]]=>2
[[1,2,2,3,3]]=>2
[[1,2,3,3,3]]=>2
[[1,3,3,3,3]]=>1
[[2,2,2,2,3]]=>2
[[2,2,2,3,3]]=>2
[[2,2,3,3,3]]=>2
[[2,3,3,3,3]]=>2
[[3,3,3,3,3]]=>1
[[1,1,1,1],[3]]=>1
[[1,1,1,2],[3]]=>2
[[1,1,1,3],[2]]=>1
[[1,1,1,3],[3]]=>2
[[1,1,2,2],[3]]=>2
[[1,1,2,3],[2]]=>2
[[1,1,2,3],[3]]=>3
[[1,1,3,3],[2]]=>1
[[1,1,3,3],[3]]=>2
[[1,2,2,2],[3]]=>2
[[1,2,2,3],[2]]=>2
[[1,2,2,3],[3]]=>3
[[1,2,3,3],[2]]=>2
[[1,2,3,3],[3]]=>3
[[1,3,3,3],[2]]=>1
[[1,3,3,3],[3]]=>2
[[2,2,2,2],[3]]=>2
[[2,2,2,3],[3]]=>3
[[2,2,3,3],[3]]=>3
[[2,3,3,3],[3]]=>3
[[1,1,1],[2,3]]=>1
[[1,1,1],[3,3]]=>1
[[1,1,2],[2,3]]=>2
[[1,1,3],[2,2]]=>1
[[1,1,2],[3,3]]=>2
[[1,1,3],[2,3]]=>2
[[1,1,3],[3,3]]=>2
[[1,2,2],[2,3]]=>2
[[1,2,2],[3,3]]=>2
[[1,2,3],[2,3]]=>3
[[1,2,3],[3,3]]=>3
[[2,2,2],[3,3]]=>2
[[2,2,3],[3,3]]=>3
[[1,1,1],[2],[3]]=>0
[[1,1,2],[2],[3]]=>1
[[1,1,3],[2],[3]]=>1
[[1,2,2],[2],[3]]=>1
[[1,2,3],[2],[3]]=>2
[[1,3,3],[2],[3]]=>1
[[1,1],[2,2],[3]]=>0
[[1,1],[2,3],[3]]=>1
[[1,2],[2,3],[3]]=>2
[[1,1,1,1,4]]=>1
[[1,1,1,2,4]]=>2
[[1,1,1,3,4]]=>2
[[1,1,1,4,4]]=>1
[[1,1,2,2,4]]=>2
[[1,1,2,3,4]]=>3
[[1,1,2,4,4]]=>2
[[1,1,3,3,4]]=>2
[[1,1,3,4,4]]=>2
[[1,1,4,4,4]]=>1
[[1,2,2,2,4]]=>2
[[1,2,2,3,4]]=>3
[[1,2,2,4,4]]=>2
[[1,2,3,3,4]]=>3
[[1,2,3,4,4]]=>3
[[1,2,4,4,4]]=>2
[[1,3,3,3,4]]=>2
[[1,3,3,4,4]]=>2
[[1,3,4,4,4]]=>2
[[1,4,4,4,4]]=>1
[[2,2,2,2,4]]=>2
[[2,2,2,3,4]]=>3
[[2,2,2,4,4]]=>2
[[2,2,3,3,4]]=>3
[[2,2,3,4,4]]=>3
[[2,2,4,4,4]]=>2
[[2,3,3,3,4]]=>3
[[2,3,3,4,4]]=>3
[[2,3,4,4,4]]=>3
[[2,4,4,4,4]]=>2
[[3,3,3,3,4]]=>2
[[3,3,3,4,4]]=>2
[[3,3,4,4,4]]=>2
[[3,4,4,4,4]]=>2
[[4,4,4,4,4]]=>1
[[1,1,1,1],[4]]=>1
[[1,1,1,2],[4]]=>2
[[1,1,1,4],[2]]=>1
[[1,1,1,3],[4]]=>2
[[1,1,1,4],[3]]=>2
[[1,1,1,4],[4]]=>2
[[1,1,2,2],[4]]=>2
[[1,1,2,4],[2]]=>2
[[1,1,2,3],[4]]=>3
[[1,1,2,4],[3]]=>3
[[1,1,3,4],[2]]=>2
[[1,1,2,4],[4]]=>3
[[1,1,4,4],[2]]=>1
[[1,1,3,3],[4]]=>2
[[1,1,3,4],[3]]=>3
[[1,1,3,4],[4]]=>3
[[1,1,4,4],[3]]=>2
[[1,1,4,4],[4]]=>2
[[1,2,2,2],[4]]=>2
[[1,2,2,4],[2]]=>2
[[1,2,2,3],[4]]=>3
[[1,2,2,4],[3]]=>3
[[1,2,3,4],[2]]=>3
[[1,2,2,4],[4]]=>3
[[1,2,4,4],[2]]=>2
[[1,2,3,3],[4]]=>3
[[1,2,3,4],[3]]=>4
[[1,3,3,4],[2]]=>2
[[1,2,3,4],[4]]=>4
[[1,2,4,4],[3]]=>3
[[1,3,4,4],[2]]=>2
[[1,2,4,4],[4]]=>3
[[1,4,4,4],[2]]=>1
[[1,3,3,3],[4]]=>2
[[1,3,3,4],[3]]=>3
[[1,3,3,4],[4]]=>3
[[1,3,4,4],[3]]=>3
[[1,3,4,4],[4]]=>3
[[1,4,4,4],[3]]=>2
[[1,4,4,4],[4]]=>2
[[2,2,2,2],[4]]=>2
[[2,2,2,3],[4]]=>3
[[2,2,2,4],[3]]=>3
[[2,2,2,4],[4]]=>3
[[2,2,3,3],[4]]=>3
[[2,2,3,4],[3]]=>4
[[2,2,3,4],[4]]=>4
[[2,2,4,4],[3]]=>3
[[2,2,4,4],[4]]=>3
[[2,3,3,3],[4]]=>3
[[2,3,3,4],[3]]=>4
[[2,3,3,4],[4]]=>4
[[2,3,4,4],[3]]=>4
[[2,3,4,4],[4]]=>4
[[2,4,4,4],[3]]=>3
[[2,4,4,4],[4]]=>3
[[3,3,3,3],[4]]=>2
[[3,3,3,4],[4]]=>3
[[3,3,4,4],[4]]=>3
[[3,4,4,4],[4]]=>3
[[1,1,1],[2,4]]=>1
[[1,1,1],[3,4]]=>2
[[1,1,1],[4,4]]=>1
[[1,1,2],[2,4]]=>2
[[1,1,4],[2,2]]=>1
[[1,1,2],[3,4]]=>3
[[1,1,3],[2,4]]=>2
[[1,1,4],[2,3]]=>2
[[1,1,2],[4,4]]=>2
[[1,1,4],[2,4]]=>2
[[1,1,3],[3,4]]=>3
[[1,1,4],[3,3]]=>2
[[1,1,3],[4,4]]=>2
[[1,1,4],[3,4]]=>3
[[1,1,4],[4,4]]=>2
[[1,2,2],[2,4]]=>2
[[1,2,2],[3,4]]=>3
[[1,2,3],[2,4]]=>3
[[1,2,4],[2,3]]=>3
[[1,2,2],[4,4]]=>2
[[1,2,4],[2,4]]=>3
[[1,2,3],[3,4]]=>4
[[1,2,4],[3,3]]=>3
[[1,3,3],[2,4]]=>2
[[1,2,3],[4,4]]=>3
[[1,2,4],[3,4]]=>4
[[1,3,4],[2,4]]=>3
[[1,2,4],[4,4]]=>3
[[1,3,3],[3,4]]=>3
[[1,3,3],[4,4]]=>2
[[1,3,4],[3,4]]=>4
[[1,3,4],[4,4]]=>3
[[2,2,2],[3,4]]=>3
[[2,2,2],[4,4]]=>2
[[2,2,3],[3,4]]=>4
[[2,2,4],[3,3]]=>3
[[2,2,3],[4,4]]=>3
[[2,2,4],[3,4]]=>4
[[2,2,4],[4,4]]=>3
[[2,3,3],[3,4]]=>4
[[2,3,3],[4,4]]=>3
[[2,3,4],[3,4]]=>5
[[2,3,4],[4,4]]=>4
[[3,3,3],[4,4]]=>2
[[3,3,4],[4,4]]=>3
[[1,1,1],[2],[4]]=>1
[[1,1,1],[3],[4]]=>2
[[1,1,2],[2],[4]]=>2
[[1,1,2],[3],[4]]=>3
[[1,1,3],[2],[4]]=>2
[[1,1,4],[2],[3]]=>1
[[1,1,4],[2],[4]]=>2
[[1,1,3],[3],[4]]=>3
[[1,1,4],[3],[4]]=>3
[[1,2,2],[2],[4]]=>2
[[1,2,2],[3],[4]]=>3
[[1,2,3],[2],[4]]=>3
[[1,2,4],[2],[3]]=>2
[[1,2,4],[2],[4]]=>3
[[1,2,3],[3],[4]]=>4
[[1,3,3],[2],[4]]=>2
[[1,3,4],[2],[3]]=>2
[[1,2,4],[3],[4]]=>4
[[1,3,4],[2],[4]]=>3
[[1,4,4],[2],[3]]=>1
[[1,4,4],[2],[4]]=>2
[[1,3,3],[3],[4]]=>3
[[1,3,4],[3],[4]]=>4
[[1,4,4],[3],[4]]=>3
[[2,2,2],[3],[4]]=>3
[[2,2,3],[3],[4]]=>4
[[2,2,4],[3],[4]]=>4
[[2,3,3],[3],[4]]=>4
[[2,3,4],[3],[4]]=>5
[[2,4,4],[3],[4]]=>4
[[1,1],[2,2],[4]]=>1
[[1,1],[2,3],[4]]=>2
[[1,1],[2,4],[3]]=>1
[[1,1],[2,4],[4]]=>2
[[1,1],[3,3],[4]]=>2
[[1,1],[3,4],[4]]=>3
[[1,2],[2,3],[4]]=>3
[[1,2],[2,4],[3]]=>2
[[1,2],[2,4],[4]]=>3
[[1,2],[3,3],[4]]=>3
[[1,3],[2,4],[3]]=>2
[[1,2],[3,4],[4]]=>4
[[1,3],[2,4],[4]]=>3
[[1,3],[3,4],[4]]=>4
[[2,2],[3,3],[4]]=>3
[[2,2],[3,4],[4]]=>4
[[2,3],[3,4],[4]]=>5
[[1,1],[2],[3],[4]]=>0
[[1,2],[2],[3],[4]]=>1
[[1,3],[2],[3],[4]]=>1
[[1,4],[2],[3],[4]]=>1
[[1,1,1,1,1,1]]=>0
[[1,1,1,1,1,2]]=>1
[[1,1,1,1,2,2]]=>1
[[1,1,1,2,2,2]]=>1
[[1,1,2,2,2,2]]=>1
[[1,2,2,2,2,2]]=>1
[[2,2,2,2,2,2]]=>1
[[1,1,1,1,1],[2]]=>0
[[1,1,1,1,2],[2]]=>1
[[1,1,1,2,2],[2]]=>1
[[1,1,2,2,2],[2]]=>1
[[1,2,2,2,2],[2]]=>1
[[1,1,1,1],[2,2]]=>0
[[1,1,1,2],[2,2]]=>1
[[1,1,2,2],[2,2]]=>1
[[1,1,1],[2,2,2]]=>0
[[1,1,1,1,1,3]]=>1
[[1,1,1,1,2,3]]=>2
[[1,1,1,1,3,3]]=>1
[[1,1,1,2,2,3]]=>2
[[1,1,1,2,3,3]]=>2
[[1,1,1,3,3,3]]=>1
[[1,1,2,2,2,3]]=>2
[[1,1,2,2,3,3]]=>2
[[1,1,2,3,3,3]]=>2
[[1,1,3,3,3,3]]=>1
[[1,2,2,2,2,3]]=>2
[[1,2,2,2,3,3]]=>2
[[1,2,2,3,3,3]]=>2
[[1,2,3,3,3,3]]=>2
[[1,3,3,3,3,3]]=>1
[[2,2,2,2,2,3]]=>2
[[2,2,2,2,3,3]]=>2
[[2,2,2,3,3,3]]=>2
[[2,2,3,3,3,3]]=>2
[[2,3,3,3,3,3]]=>2
[[3,3,3,3,3,3]]=>1
[[1,1,1,1,1],[3]]=>1
[[1,1,1,1,2],[3]]=>2
[[1,1,1,1,3],[2]]=>1
[[1,1,1,1,3],[3]]=>2
[[1,1,1,2,2],[3]]=>2
[[1,1,1,2,3],[2]]=>2
[[1,1,1,2,3],[3]]=>3
[[1,1,1,3,3],[2]]=>1
[[1,1,1,3,3],[3]]=>2
[[1,1,2,2,2],[3]]=>2
[[1,1,2,2,3],[2]]=>2
[[1,1,2,2,3],[3]]=>3
[[1,1,2,3,3],[2]]=>2
[[1,1,2,3,3],[3]]=>3
[[1,1,3,3,3],[2]]=>1
[[1,1,3,3,3],[3]]=>2
[[1,2,2,2,2],[3]]=>2
[[1,2,2,2,3],[2]]=>2
[[1,2,2,2,3],[3]]=>3
[[1,2,2,3,3],[2]]=>2
[[1,2,2,3,3],[3]]=>3
[[1,2,3,3,3],[2]]=>2
[[1,2,3,3,3],[3]]=>3
[[1,3,3,3,3],[2]]=>1
[[1,3,3,3,3],[3]]=>2
[[2,2,2,2,2],[3]]=>2
[[2,2,2,2,3],[3]]=>3
[[2,2,2,3,3],[3]]=>3
[[2,2,3,3,3],[3]]=>3
[[2,3,3,3,3],[3]]=>3
[[1,1,1,1],[2,3]]=>1
[[1,1,1,1],[3,3]]=>1
[[1,1,1,2],[2,3]]=>2
[[1,1,1,3],[2,2]]=>1
[[1,1,1,2],[3,3]]=>2
[[1,1,1,3],[2,3]]=>2
[[1,1,1,3],[3,3]]=>2
[[1,1,2,2],[2,3]]=>2
[[1,1,2,3],[2,2]]=>2
[[1,1,2,2],[3,3]]=>2
[[1,1,2,3],[2,3]]=>3
[[1,1,3,3],[2,2]]=>1
[[1,1,2,3],[3,3]]=>3
[[1,1,3,3],[2,3]]=>2
[[1,1,3,3],[3,3]]=>2
[[1,2,2,2],[2,3]]=>2
[[1,2,2,2],[3,3]]=>2
[[1,2,2,3],[2,3]]=>3
[[1,2,2,3],[3,3]]=>3
[[1,2,3,3],[2,3]]=>3
[[1,2,3,3],[3,3]]=>3
[[2,2,2,2],[3,3]]=>2
[[2,2,2,3],[3,3]]=>3
[[2,2,3,3],[3,3]]=>3
[[1,1,1,1],[2],[3]]=>0
[[1,1,1,2],[2],[3]]=>1
[[1,1,1,3],[2],[3]]=>1
[[1,1,2,2],[2],[3]]=>1
[[1,1,2,3],[2],[3]]=>2
[[1,1,3,3],[2],[3]]=>1
[[1,2,2,2],[2],[3]]=>1
[[1,2,2,3],[2],[3]]=>2
[[1,2,3,3],[2],[3]]=>2
[[1,3,3,3],[2],[3]]=>1
[[1,1,1],[2,2,3]]=>1
[[1,1,1],[2,3,3]]=>1
[[1,1,1],[3,3,3]]=>1
[[1,1,2],[2,2,3]]=>2
[[1,1,2],[2,3,3]]=>2
[[1,1,2],[3,3,3]]=>2
[[1,2,2],[2,3,3]]=>2
[[1,2,2],[3,3,3]]=>2
[[2,2,2],[3,3,3]]=>2
[[1,1,1],[2,2],[3]]=>0
[[1,1,1],[2,3],[3]]=>1
[[1,1,2],[2,2],[3]]=>1
[[1,1,2],[2,3],[3]]=>2
[[1,1,3],[2,2],[3]]=>1
[[1,1,3],[2,3],[3]]=>2
[[1,2,2],[2,3],[3]]=>2
[[1,2,3],[2,3],[3]]=>3
[[1,1],[2,2],[3,3]]=>0
[[1,1,1,1,1,4]]=>1
[[1,1,1,1,2,4]]=>2
[[1,1,1,1,3,4]]=>2
[[1,1,1,1,4,4]]=>1
[[1,1,1,2,2,4]]=>2
[[1,1,1,2,3,4]]=>3
[[1,1,1,2,4,4]]=>2
[[1,1,1,3,3,4]]=>2
[[1,1,1,3,4,4]]=>2
[[1,1,1,4,4,4]]=>1
[[1,1,2,2,2,4]]=>2
[[1,1,2,2,3,4]]=>3
[[1,1,2,2,4,4]]=>2
[[1,1,2,3,3,4]]=>3
[[1,1,2,3,4,4]]=>3
[[1,1,2,4,4,4]]=>2
[[1,1,3,3,3,4]]=>2
[[1,1,3,3,4,4]]=>2
[[1,1,3,4,4,4]]=>2
[[1,1,4,4,4,4]]=>1
[[1,2,2,2,2,4]]=>2
[[1,2,2,2,3,4]]=>3
[[1,2,2,2,4,4]]=>2
[[1,2,2,3,3,4]]=>3
[[1,2,2,3,4,4]]=>3
[[1,2,2,4,4,4]]=>2
[[1,2,3,3,3,4]]=>3
[[1,2,3,3,4,4]]=>3
[[1,2,3,4,4,4]]=>3
[[1,2,4,4,4,4]]=>2
[[1,3,3,3,3,4]]=>2
[[1,3,3,3,4,4]]=>2
[[1,3,3,4,4,4]]=>2
[[1,3,4,4,4,4]]=>2
[[1,4,4,4,4,4]]=>1
[[2,2,2,2,2,4]]=>2
[[2,2,2,2,3,4]]=>3
[[2,2,2,2,4,4]]=>2
[[2,2,2,3,3,4]]=>3
[[2,2,2,3,4,4]]=>3
[[2,2,2,4,4,4]]=>2
[[2,2,3,3,3,4]]=>3
[[2,2,3,3,4,4]]=>3
[[2,2,3,4,4,4]]=>3
[[2,2,4,4,4,4]]=>2
[[2,3,3,3,3,4]]=>3
[[2,3,3,3,4,4]]=>3
[[2,3,3,4,4,4]]=>3
[[2,3,4,4,4,4]]=>3
[[2,4,4,4,4,4]]=>2
[[3,3,3,3,3,4]]=>2
[[3,3,3,3,4,4]]=>2
[[3,3,3,4,4,4]]=>2
[[3,3,4,4,4,4]]=>2
[[3,4,4,4,4,4]]=>2
[[4,4,4,4,4,4]]=>1
[[1,1,1,1,1],[4]]=>1
[[1,1,1,1,2],[4]]=>2
[[1,1,1,1,4],[2]]=>1
[[1,1,1,1,3],[4]]=>2
[[1,1,1,1,4],[3]]=>2
[[1,1,1,1,4],[4]]=>2
[[1,1,1,2,2],[4]]=>2
[[1,1,1,2,4],[2]]=>2
[[1,1,1,2,3],[4]]=>3
[[1,1,1,2,4],[3]]=>3
[[1,1,1,3,4],[2]]=>2
[[1,1,1,2,4],[4]]=>3
[[1,1,1,4,4],[2]]=>1
[[1,1,1,3,3],[4]]=>2
[[1,1,1,3,4],[3]]=>3
[[1,1,1,3,4],[4]]=>3
[[1,1,1,4,4],[3]]=>2
[[1,1,1,4,4],[4]]=>2
[[1,1,2,2,2],[4]]=>2
[[1,1,2,2,4],[2]]=>2
[[1,1,2,2,3],[4]]=>3
[[1,1,2,2,4],[3]]=>3
[[1,1,2,3,4],[2]]=>3
[[1,1,2,2,4],[4]]=>3
[[1,1,2,4,4],[2]]=>2
[[1,1,2,3,3],[4]]=>3
[[1,1,2,3,4],[3]]=>4
[[1,1,3,3,4],[2]]=>2
[[1,1,2,3,4],[4]]=>4
[[1,1,2,4,4],[3]]=>3
[[1,1,3,4,4],[2]]=>2
[[1,1,2,4,4],[4]]=>3
[[1,1,4,4,4],[2]]=>1
[[1,1,3,3,3],[4]]=>2
[[1,1,3,3,4],[3]]=>3
[[1,1,3,3,4],[4]]=>3
[[1,1,3,4,4],[3]]=>3
[[1,1,3,4,4],[4]]=>3
[[1,1,4,4,4],[3]]=>2
[[1,1,4,4,4],[4]]=>2
[[1,2,2,2,2],[4]]=>2
[[1,2,2,2,4],[2]]=>2
[[1,2,2,2,3],[4]]=>3
[[1,2,2,2,4],[3]]=>3
[[1,2,2,3,4],[2]]=>3
[[1,2,2,2,4],[4]]=>3
[[1,2,2,4,4],[2]]=>2
[[1,2,2,3,3],[4]]=>3
[[1,2,2,3,4],[3]]=>4
[[1,2,3,3,4],[2]]=>3
[[1,2,2,3,4],[4]]=>4
[[1,2,2,4,4],[3]]=>3
[[1,2,3,4,4],[2]]=>3
[[1,2,2,4,4],[4]]=>3
[[1,2,4,4,4],[2]]=>2
[[1,2,3,3,3],[4]]=>3
[[1,2,3,3,4],[3]]=>4
[[1,3,3,3,4],[2]]=>2
[[1,2,3,3,4],[4]]=>4
[[1,2,3,4,4],[3]]=>4
[[1,3,3,4,4],[2]]=>2
[[1,2,3,4,4],[4]]=>4
[[1,2,4,4,4],[3]]=>3
[[1,3,4,4,4],[2]]=>2
[[1,2,4,4,4],[4]]=>3
[[1,4,4,4,4],[2]]=>1
[[1,3,3,3,3],[4]]=>2
[[1,3,3,3,4],[3]]=>3
[[1,3,3,3,4],[4]]=>3
[[1,3,3,4,4],[3]]=>3
[[1,3,3,4,4],[4]]=>3
[[1,3,4,4,4],[3]]=>3
[[1,3,4,4,4],[4]]=>3
[[1,4,4,4,4],[3]]=>2
[[1,4,4,4,4],[4]]=>2
[[2,2,2,2,2],[4]]=>2
[[2,2,2,2,3],[4]]=>3
[[2,2,2,2,4],[3]]=>3
[[2,2,2,2,4],[4]]=>3
[[2,2,2,3,3],[4]]=>3
[[2,2,2,3,4],[3]]=>4
[[2,2,2,3,4],[4]]=>4
[[2,2,2,4,4],[3]]=>3
[[2,2,2,4,4],[4]]=>3
[[2,2,3,3,3],[4]]=>3
[[2,2,3,3,4],[3]]=>4
[[2,2,3,3,4],[4]]=>4
[[2,2,3,4,4],[3]]=>4
[[2,2,3,4,4],[4]]=>4
[[2,2,4,4,4],[3]]=>3
[[2,2,4,4,4],[4]]=>3
[[2,3,3,3,3],[4]]=>3
[[2,3,3,3,4],[3]]=>4
[[2,3,3,3,4],[4]]=>4
[[2,3,3,4,4],[3]]=>4
[[2,3,3,4,4],[4]]=>4
[[2,3,4,4,4],[3]]=>4
[[2,3,4,4,4],[4]]=>4
[[2,4,4,4,4],[3]]=>3
[[2,4,4,4,4],[4]]=>3
[[3,3,3,3,3],[4]]=>2
[[3,3,3,3,4],[4]]=>3
[[3,3,3,4,4],[4]]=>3
[[3,3,4,4,4],[4]]=>3
[[3,4,4,4,4],[4]]=>3
[[1,1,1,1],[2,4]]=>1
[[1,1,1,1],[3,4]]=>2
[[1,1,1,1],[4,4]]=>1
[[1,1,1,2],[2,4]]=>2
[[1,1,1,4],[2,2]]=>1
[[1,1,1,2],[3,4]]=>3
[[1,1,1,3],[2,4]]=>2
[[1,1,1,4],[2,3]]=>2
[[1,1,1,2],[4,4]]=>2
[[1,1,1,4],[2,4]]=>2
[[1,1,1,3],[3,4]]=>3
[[1,1,1,4],[3,3]]=>2
[[1,1,1,3],[4,4]]=>2
[[1,1,1,4],[3,4]]=>3
[[1,1,1,4],[4,4]]=>2
[[1,1,2,2],[2,4]]=>2
[[1,1,2,4],[2,2]]=>2
[[1,1,2,2],[3,4]]=>3
[[1,1,2,3],[2,4]]=>3
[[1,1,2,4],[2,3]]=>3
[[1,1,3,4],[2,2]]=>2
[[1,1,2,2],[4,4]]=>2
[[1,1,2,4],[2,4]]=>3
[[1,1,4,4],[2,2]]=>1
[[1,1,2,3],[3,4]]=>4
[[1,1,2,4],[3,3]]=>3
[[1,1,3,3],[2,4]]=>2
[[1,1,3,4],[2,3]]=>3
[[1,1,2,3],[4,4]]=>3
[[1,1,2,4],[3,4]]=>4
[[1,1,3,4],[2,4]]=>3
[[1,1,4,4],[2,3]]=>2
[[1,1,2,4],[4,4]]=>3
[[1,1,4,4],[2,4]]=>2
[[1,1,3,3],[3,4]]=>3
[[1,1,3,4],[3,3]]=>3
[[1,1,3,3],[4,4]]=>2
[[1,1,3,4],[3,4]]=>4
[[1,1,4,4],[3,3]]=>2
[[1,1,3,4],[4,4]]=>3
[[1,1,4,4],[3,4]]=>3
[[1,1,4,4],[4,4]]=>2
[[1,2,2,2],[2,4]]=>2
[[1,2,2,2],[3,4]]=>3
[[1,2,2,3],[2,4]]=>3
[[1,2,2,4],[2,3]]=>3
[[1,2,2,2],[4,4]]=>2
[[1,2,2,4],[2,4]]=>3
[[1,2,2,3],[3,4]]=>4
[[1,2,2,4],[3,3]]=>3
[[1,2,3,3],[2,4]]=>3
[[1,2,3,4],[2,3]]=>4
[[1,2,2,3],[4,4]]=>3
[[1,2,2,4],[3,4]]=>4
[[1,2,3,4],[2,4]]=>4
[[1,2,4,4],[2,3]]=>3
[[1,2,2,4],[4,4]]=>3
[[1,2,4,4],[2,4]]=>3
[[1,2,3,3],[3,4]]=>4
[[1,2,3,4],[3,3]]=>4
[[1,3,3,3],[2,4]]=>2
[[1,2,3,3],[4,4]]=>3
[[1,2,3,4],[3,4]]=>5
[[1,2,4,4],[3,3]]=>3
[[1,3,3,4],[2,4]]=>3
[[1,2,3,4],[4,4]]=>4
[[1,2,4,4],[3,4]]=>4
[[1,3,4,4],[2,4]]=>3
[[1,2,4,4],[4,4]]=>3
[[1,3,3,3],[3,4]]=>3
[[1,3,3,3],[4,4]]=>2
[[1,3,3,4],[3,4]]=>4
[[1,3,3,4],[4,4]]=>3
[[1,3,4,4],[3,4]]=>4
[[1,3,4,4],[4,4]]=>3
[[2,2,2,2],[3,4]]=>3
[[2,2,2,2],[4,4]]=>2
[[2,2,2,3],[3,4]]=>4
[[2,2,2,4],[3,3]]=>3
[[2,2,2,3],[4,4]]=>3
[[2,2,2,4],[3,4]]=>4
[[2,2,2,4],[4,4]]=>3
[[2,2,3,3],[3,4]]=>4
[[2,2,3,4],[3,3]]=>4
[[2,2,3,3],[4,4]]=>3
[[2,2,3,4],[3,4]]=>5
[[2,2,4,4],[3,3]]=>3
[[2,2,3,4],[4,4]]=>4
[[2,2,4,4],[3,4]]=>4
[[2,2,4,4],[4,4]]=>3
[[2,3,3,3],[3,4]]=>4
[[2,3,3,3],[4,4]]=>3
[[2,3,3,4],[3,4]]=>5
[[2,3,3,4],[4,4]]=>4
[[2,3,4,4],[3,4]]=>5
[[2,3,4,4],[4,4]]=>4
[[3,3,3,3],[4,4]]=>2
[[3,3,3,4],[4,4]]=>3
[[3,3,4,4],[4,4]]=>3
[[1,1,1,1],[2],[4]]=>1
[[1,1,1,1],[3],[4]]=>2
[[1,1,1,2],[2],[4]]=>2
[[1,1,1,2],[3],[4]]=>3
[[1,1,1,3],[2],[4]]=>2
[[1,1,1,4],[2],[3]]=>1
[[1,1,1,4],[2],[4]]=>2
[[1,1,1,3],[3],[4]]=>3
[[1,1,1,4],[3],[4]]=>3
[[1,1,2,2],[2],[4]]=>2
[[1,1,2,2],[3],[4]]=>3
[[1,1,2,3],[2],[4]]=>3
[[1,1,2,4],[2],[3]]=>2
[[1,1,2,4],[2],[4]]=>3
[[1,1,2,3],[3],[4]]=>4
[[1,1,3,3],[2],[4]]=>2
[[1,1,3,4],[2],[3]]=>2
[[1,1,2,4],[3],[4]]=>4
[[1,1,3,4],[2],[4]]=>3
[[1,1,4,4],[2],[3]]=>1
[[1,1,4,4],[2],[4]]=>2
[[1,1,3,3],[3],[4]]=>3
[[1,1,3,4],[3],[4]]=>4
[[1,1,4,4],[3],[4]]=>3
[[1,2,2,2],[2],[4]]=>2
[[1,2,2,2],[3],[4]]=>3
[[1,2,2,3],[2],[4]]=>3
[[1,2,2,4],[2],[3]]=>2
[[1,2,2,4],[2],[4]]=>3
[[1,2,2,3],[3],[4]]=>4
[[1,2,3,3],[2],[4]]=>3
[[1,2,3,4],[2],[3]]=>3
[[1,2,2,4],[3],[4]]=>4
[[1,2,3,4],[2],[4]]=>4
[[1,2,4,4],[2],[3]]=>2
[[1,2,4,4],[2],[4]]=>3
[[1,2,3,3],[3],[4]]=>4
[[1,3,3,3],[2],[4]]=>2
[[1,3,3,4],[2],[3]]=>2
[[1,2,3,4],[3],[4]]=>5
[[1,3,3,4],[2],[4]]=>3
[[1,3,4,4],[2],[3]]=>2
[[1,2,4,4],[3],[4]]=>4
[[1,3,4,4],[2],[4]]=>3
[[1,4,4,4],[2],[3]]=>1
[[1,4,4,4],[2],[4]]=>2
[[1,3,3,3],[3],[4]]=>3
[[1,3,3,4],[3],[4]]=>4
[[1,3,4,4],[3],[4]]=>4
[[1,4,4,4],[3],[4]]=>3
[[2,2,2,2],[3],[4]]=>3
[[2,2,2,3],[3],[4]]=>4
[[2,2,2,4],[3],[4]]=>4
[[2,2,3,3],[3],[4]]=>4
[[2,2,3,4],[3],[4]]=>5
[[2,2,4,4],[3],[4]]=>4
[[2,3,3,3],[3],[4]]=>4
[[2,3,3,4],[3],[4]]=>5
[[2,3,4,4],[3],[4]]=>5
[[2,4,4,4],[3],[4]]=>4
[[1,1,1],[2,2,4]]=>1
[[1,1,1],[2,3,4]]=>2
[[1,1,1],[2,4,4]]=>1
[[1,1,1],[3,3,4]]=>2
[[1,1,1],[3,4,4]]=>2
[[1,1,1],[4,4,4]]=>1
[[1,1,2],[2,2,4]]=>2
[[1,1,2],[2,3,4]]=>3
[[1,1,3],[2,2,4]]=>2
[[1,1,2],[2,4,4]]=>2
[[1,1,2],[3,3,4]]=>3
[[1,1,3],[2,3,4]]=>3
[[1,1,2],[3,4,4]]=>3
[[1,1,3],[2,4,4]]=>2
[[1,1,2],[4,4,4]]=>2
[[1,1,3],[3,3,4]]=>3
[[1,1,3],[3,4,4]]=>3
[[1,1,3],[4,4,4]]=>2
[[1,2,2],[2,3,4]]=>3
[[1,2,2],[2,4,4]]=>2
[[1,2,2],[3,3,4]]=>3
[[1,2,3],[2,3,4]]=>4
[[1,2,2],[3,4,4]]=>3
[[1,2,3],[2,4,4]]=>3
[[1,2,2],[4,4,4]]=>2
[[1,2,3],[3,3,4]]=>4
[[1,2,3],[3,4,4]]=>4
[[1,3,3],[2,4,4]]=>2
[[1,2,3],[4,4,4]]=>3
[[1,3,3],[3,4,4]]=>3
[[1,3,3],[4,4,4]]=>2
[[2,2,2],[3,3,4]]=>3
[[2,2,2],[3,4,4]]=>3
[[2,2,2],[4,4,4]]=>2
[[2,2,3],[3,3,4]]=>4
[[2,2,3],[3,4,4]]=>4
[[2,2,3],[4,4,4]]=>3
[[2,3,3],[3,4,4]]=>4
[[2,3,3],[4,4,4]]=>3
[[3,3,3],[4,4,4]]=>2
[[1,1,1],[2,2],[4]]=>1
[[1,1,1],[2,3],[4]]=>2
[[1,1,1],[2,4],[3]]=>1
[[1,1,1],[2,4],[4]]=>2
[[1,1,1],[3,3],[4]]=>2
[[1,1,1],[3,4],[4]]=>3
[[1,1,2],[2,2],[4]]=>2
[[1,1,2],[2,3],[4]]=>3
[[1,1,2],[2,4],[3]]=>2
[[1,1,3],[2,2],[4]]=>2
[[1,1,4],[2,2],[3]]=>1
[[1,1,2],[2,4],[4]]=>3
[[1,1,4],[2,2],[4]]=>2
[[1,1,2],[3,3],[4]]=>3
[[1,1,3],[2,3],[4]]=>3
[[1,1,3],[2,4],[3]]=>2
[[1,1,4],[2,3],[3]]=>2
[[1,1,2],[3,4],[4]]=>4
[[1,1,3],[2,4],[4]]=>3
[[1,1,4],[2,3],[4]]=>3
[[1,1,4],[2,4],[3]]=>2
[[1,1,4],[2,4],[4]]=>3
[[1,1,3],[3,3],[4]]=>3
[[1,1,3],[3,4],[4]]=>4
[[1,1,4],[3,3],[4]]=>3
[[1,1,4],[3,4],[4]]=>4
[[1,2,2],[2,3],[4]]=>3
[[1,2,2],[2,4],[3]]=>2
[[1,2,2],[2,4],[4]]=>3
[[1,2,2],[3,3],[4]]=>3
[[1,2,3],[2,3],[4]]=>4
[[1,2,3],[2,4],[3]]=>3
[[1,2,4],[2,3],[3]]=>3
[[1,2,2],[3,4],[4]]=>4
[[1,2,3],[2,4],[4]]=>4
[[1,2,4],[2,3],[4]]=>4
[[1,2,4],[2,4],[3]]=>3
[[1,2,4],[2,4],[4]]=>4
[[1,2,3],[3,3],[4]]=>4
[[1,3,3],[2,4],[3]]=>2
[[1,2,3],[3,4],[4]]=>5
[[1,2,4],[3,3],[4]]=>4
[[1,3,3],[2,4],[4]]=>3
[[1,3,4],[2,4],[3]]=>3
[[1,2,4],[3,4],[4]]=>5
[[1,3,4],[2,4],[4]]=>4
[[1,3,3],[3,4],[4]]=>4
[[1,3,4],[3,4],[4]]=>5
[[2,2,2],[3,3],[4]]=>3
[[2,2,2],[3,4],[4]]=>4
[[2,2,3],[3,3],[4]]=>4
[[2,2,3],[3,4],[4]]=>5
[[2,2,4],[3,3],[4]]=>4
[[2,2,4],[3,4],[4]]=>5
[[2,3,3],[3,4],[4]]=>5
[[2,3,4],[3,4],[4]]=>6
[[1,1,1],[2],[3],[4]]=>0
[[1,1,2],[2],[3],[4]]=>1
[[1,1,3],[2],[3],[4]]=>1
[[1,1,4],[2],[3],[4]]=>1
[[1,2,2],[2],[3],[4]]=>1
[[1,2,3],[2],[3],[4]]=>2
[[1,2,4],[2],[3],[4]]=>2
[[1,3,3],[2],[3],[4]]=>1
[[1,3,4],[2],[3],[4]]=>2
[[1,4,4],[2],[3],[4]]=>1
[[1,1],[2,2],[3,4]]=>1
[[1,1],[2,2],[4,4]]=>1
[[1,1],[2,3],[3,4]]=>2
[[1,1],[2,3],[4,4]]=>2
[[1,1],[3,3],[4,4]]=>2
[[1,2],[2,3],[3,4]]=>3
[[1,2],[2,3],[4,4]]=>3
[[1,2],[3,3],[4,4]]=>3
[[2,2],[3,3],[4,4]]=>3
[[1,1],[2,2],[3],[4]]=>0
[[1,1],[2,3],[3],[4]]=>1
[[1,1],[2,4],[3],[4]]=>1
[[1,2],[2,3],[3],[4]]=>2
[[1,2],[2,4],[3],[4]]=>2
[[1,3],[2,4],[3],[4]]=>2
[[1,1,1,1,1,1,1]]=>0
[[1,1,1,1,1,1,2]]=>1
[[1,1,1,1,1,2,2]]=>1
[[1,1,1,1,2,2,2]]=>1
[[1,1,1,2,2,2,2]]=>1
[[1,1,2,2,2,2,2]]=>1
[[1,2,2,2,2,2,2]]=>1
[[2,2,2,2,2,2,2]]=>1
[[1,1,1,1,1,1],[2]]=>0
[[1,1,1,1,1,2],[2]]=>1
[[1,1,1,1,2,2],[2]]=>1
[[1,1,1,2,2,2],[2]]=>1
[[1,1,2,2,2,2],[2]]=>1
[[1,1,1,1,1,1,3]]=>1
[[1,1,1,1,1,2,3]]=>2
[[1,1,1,1,1,3,3]]=>1
[[1,1,1,1,2,2,3]]=>2
[[1,1,1,1,2,3,3]]=>2
[[1,1,1,1,3,3,3]]=>1
[[1,1,1,2,2,2,3]]=>2
[[1,1,1,2,2,3,3]]=>2
[[1,1,1,2,3,3,3]]=>2
[[1,1,1,3,3,3,3]]=>1
[[1,1,2,2,2,2,3]]=>2
[[1,1,2,2,2,3,3]]=>2
[[1,1,2,2,3,3,3]]=>2
[[1,1,2,3,3,3,3]]=>2
[[1,1,3,3,3,3,3]]=>1
[[1,2,2,2,2,2,3]]=>2
[[1,2,2,2,2,3,3]]=>2
[[1,2,2,2,3,3,3]]=>2
[[1,2,2,3,3,3,3]]=>2
[[1,2,3,3,3,3,3]]=>2
[[1,3,3,3,3,3,3]]=>1
[[2,2,2,2,2,2,3]]=>2
[[2,2,2,2,2,3,3]]=>2
[[2,2,2,2,3,3,3]]=>2
[[2,2,2,3,3,3,3]]=>2
[[2,2,3,3,3,3,3]]=>2
[[2,3,3,3,3,3,3]]=>2
[[3,3,3,3,3,3,3]]=>1
[[1,1,1,1,1,1],[3]]=>1
[[1,1,1,1,1,2],[3]]=>2
[[1,1,1,1,1,3],[2]]=>1
[[1,1,1,1,1,3],[3]]=>2
[[1,1,1,1,2,2],[3]]=>2
[[1,1,1,1,2,3],[2]]=>2
[[1,1,1,1,2,3],[3]]=>3
[[1,1,1,1,3,3],[2]]=>1
[[1,1,1,1,3,3],[3]]=>2
[[1,1,1,2,2,2],[3]]=>2
[[1,1,1,2,2,3],[2]]=>2
[[1,1,1,2,2,3],[3]]=>3
[[1,1,1,2,3,3],[2]]=>2
[[1,1,1,2,3,3],[3]]=>3
[[1,1,1,3,3,3],[2]]=>1
[[1,1,1,3,3,3],[3]]=>2
[[1,1,2,2,2,2],[3]]=>2
[[1,1,2,2,2,3],[2]]=>2
[[1,1,2,2,2,3],[3]]=>3
[[1,1,2,2,3,3],[2]]=>2
[[1,1,2,2,3,3],[3]]=>3
[[1,1,2,3,3,3],[2]]=>2
[[1,1,1,1,1,1,4]]=>1
[[1,1,1,1,1,2,4]]=>2
[[1,1,1,1,1,3,4]]=>2
[[1,1,1,1,1,4,4]]=>1
[[1,1,1,1,2,2,4]]=>2
[[1,1,1,1,2,3,4]]=>3
[[1,1,1,1,2,4,4]]=>2
[[1,1,1,1,3,3,4]]=>2
[[1,1,1,1,3,4,4]]=>2
[[1,1,1,1,4,4,4]]=>1
[[1,1,1,2,2,2,4]]=>2
[[1,1,1,2,2,3,4]]=>3
[[1,1,1,2,2,4,4]]=>2
[[1,1,1,2,3,3,4]]=>3
[[1,1,1,2,3,4,4]]=>3
[[1,1,1,2,4,4,4]]=>2
[[1,1,1,3,3,3,4]]=>2
[[1,1,1,3,3,4,4]]=>2
[[1,1,1,3,4,4,4]]=>2
[[1,1,1,4,4,4,4]]=>1
[[1,1,2,2,2,2,4]]=>2
[[1,1,2,2,2,3,4]]=>3
[[1,1,2,2,2,4,4]]=>2
[[1,1,2,2,3,3,4]]=>3
[[1,1,2,2,3,4,4]]=>3
[[1,1,2,2,4,4,4]]=>2
[[1,1,2,3,3,3,4]]=>3
[[1,1,2,3,3,4,4]]=>3
[[1,1,2,3,4,4,4]]=>3
[[1,1,2,4,4,4,4]]=>2
[[1,1,3,3,3,3,4]]=>2
[[1,1,3,3,3,4,4]]=>2
[[1,1,3,3,4,4,4]]=>2
[[1,1,3,4,4,4,4]]=>2
[[1,1,4,4,4,4,4]]=>1
[[1,2,2,2,2,2,4]]=>2
[[1,2,2,2,2,3,4]]=>3
[[1,2,2,2,2,4,4]]=>2
[[1,2,2,2,3,3,4]]=>3
[[1,2,2,2,3,4,4]]=>3
[[1,2,2,2,4,4,4]]=>2
[[1,2,2,3,3,3,4]]=>3
[[1,2,2,3,3,4,4]]=>3
[[1,2,2,3,4,4,4]]=>3
[[1,2,2,4,4,4,4]]=>2
[[1,2,3,3,3,3,4]]=>3
[[1,2,3,3,3,4,4]]=>3
[[1,2,3,3,4,4,4]]=>3
[[1,2,3,4,4,4,4]]=>3
[[1,2,4,4,4,4,4]]=>2
[[1,3,3,3,3,3,4]]=>2
[[1,3,3,3,3,4,4]]=>2
[[1,3,3,3,4,4,4]]=>2
[[1,3,3,4,4,4,4]]=>2
[[1,3,4,4,4,4,4]]=>2
[[1,4,4,4,4,4,4]]=>1
[[2,2,2,2,2,2,4]]=>2
[[2,2,2,2,2,3,4]]=>3
[[2,2,2,2,2,4,4]]=>2
[[2,2,2,2,3,3,4]]=>3
[[2,2,2,2,3,4,4]]=>3
[[2,2,2,2,4,4,4]]=>2
[[2,2,2,3,3,3,4]]=>3
[[2,2,2,3,3,4,4]]=>3
[[2,2,2,3,4,4,4]]=>3
[[2,2,2,4,4,4,4]]=>2
[[2,2,3,3,3,3,4]]=>3
[[2,2,3,3,3,4,4]]=>3
[[2,2,3,3,4,4,4]]=>3
[[2,2,3,4,4,4,4]]=>3
[[2,2,4,4,4,4,4]]=>2
[[2,3,3,3,3,3,4]]=>3
[[2,3,3,3,3,4,4]]=>3
[[2,3,3,3,4,4,4]]=>3
[[2,3,3,4,4,4,4]]=>3
[[2,3,4,4,4,4,4]]=>3
[[2,4,4,4,4,4,4]]=>2
[[3,3,3,3,3,3,4]]=>2
[[3,3,3,3,3,4,4]]=>2
[[3,3,3,3,4,4,4]]=>2
[[3,3,3,4,4,4,4]]=>2
[[3,3,4,4,4,4,4]]=>2
[[3,4,4,4,4,4,4]]=>2
[[4,4,4,4,4,4,4]]=>1
[[1,1,1,1,1,1],[4]]=>1
[[1,1,1,1,1,2],[4]]=>2
[[1,1,1,1,1,4],[2]]=>1
[[1,1,1,1,1,3],[4]]=>2
[[1,1,1,1,1,4],[3]]=>2
[[1,1,1,1,1,4],[4]]=>2
[[1,1,1,1,2,2],[4]]=>2
[[1,1,1,1,2,4],[2]]=>2
[[1,1,1,1,2,3],[4]]=>3
[[1,1,1,1,2,4],[3]]=>3
[[1,1,1,1,3,4],[2]]=>2
[[1,1,1,1,2,4],[4]]=>3
[[1,1,1,1,4,4],[2]]=>1
[[1,1,1,1,3,3],[4]]=>2
[[1,1,1,1,3,4],[3]]=>3
[[1,1,1,1,3,4],[4]]=>3
[[1,1,1,1,4,4],[3]]=>2
[[1,1,1,1,4,4],[4]]=>2
[[1,1,1,2,2,2],[4]]=>2
[[1,1,1,2,2,4],[2]]=>2
[[1,1,1,2,2,3],[4]]=>3
[[1,1,1,2,2,4],[3]]=>3
[[1,1,1,2,3,4],[2]]=>3
[[1,1,1,2,2,4],[4]]=>3
[[1,1,1,2,4,4],[2]]=>2
[[1,1,1,2,3,3],[4]]=>3
[[1,1,1,2,3,4],[3]]=>4
[[1,1,1,3,3,4],[2]]=>2
[[1,1,1,2,3,4],[4]]=>4
[[1,1,1,2,4,4],[3]]=>3
[[1,1,1,3,4,4],[2]]=>2
[[1,1,1,2,4,4],[4]]=>3
[[1,1,1,4,4,4],[2]]=>1
[[1,1,1,3,3,3],[4]]=>2
[[1,1,1,3,3,4],[3]]=>3
[[1,1,1,3,3,4],[4]]=>3
[[1,1,1,3,4,4],[3]]=>3
[[1,1,1,3,4,4],[4]]=>3
[[1,1,1,4,4,4],[3]]=>2
[[1,1,1,4,4,4],[4]]=>2
[[1,1,2,2,2,2],[4]]=>2
[[1,1,2,2,2,4],[2]]=>2
[[1,1,2,2,2,3],[4]]=>3
[[1,1,2,2,2,4],[3]]=>3
[[1,1,2,2,3,4],[2]]=>3
[[1,1,2,2,2,4],[4]]=>3
[[1,1,2,2,4,4],[2]]=>2
[[1,1,2,2,3,3],[4]]=>3
[[1,1,2,2,3,4],[3]]=>4
[[1,1,2,3,3,4],[2]]=>3
[[1,1,2,2,3,4],[4]]=>4
[[1,1,2,2,4,4],[3]]=>3
[[1,1,2,3,4,4],[2]]=>3
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Description
The segment statistic of a semistandard tableau.
Let T be a tableau. A k-segment of T (in the ith row) is defined to be a maximal consecutive sequence of k-boxes in the ith row. Note that the possible i-boxes in the ith row are not considered to be i-segments. Then seg(T) is the total number of k-segments in T as k varies over all possible values.
Let T be a tableau. A k-segment of T (in the ith row) is defined to be a maximal consecutive sequence of k-boxes in the ith row. Note that the possible i-boxes in the ith row are not considered to be i-segments. Then seg(T) is the total number of k-segments in T as k varies over all possible values.
References
[1] Salisbury, B. The flush statistic on semistandard Young tableaux arXiv:1401.1185
Code
def statistic(x): return x.seg()
Created
Jan 13, 2014 at 21:21 by Ben Salisbury
Updated
Oct 19, 2015 at 16:36 by Christian Stump
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