mutableYoungTableau -- constructor for type MutableYoungTableau

• Usage:

  mutableYoungTableau(lam, mu, entryList)

  mutableYoungTableau((lam,mu),entryList)

• Inputs:
  • lam, an instance of the type Partition, the outer shape $\lambda$.
  • mu, an instance of the type Partition, the inner shape $\mu$. If not given, then it is assumed to be the $0$ partition.
  • entryList, a list, the filling of the boxes. If not given, then box entries are assumed to be the empty string "".
• Outputs:
  • T, an instance of the type MutableYoungTableau, a skew Young tableau of shape $\lambda/\mu$ with the given (mutable) filling.
• Consequences:

  • The list of entries has length equal to $\sum_{i=1}^{\ell(\lambda)}|\lambda_i-\mu_i|$. E.g., if $\lambda=(2)$ and $\mu=(5)$, then the entry list must have length $3$.
  • None of the entries are null.

i1 : T = mutableYoungTableau(new Partition from {4,2,1}, new Partition from {1}, toList(1..6))

         ┌───┬───┬───┐
o1 =     │ 1 │ 2 │ 3 │
     ┌───┼───┼───┴───┘
     │ 4 │ 5 │        
     ├───┼───┘        
     │ 6 │            
     └───┘            

o1 : MutableYoungTableau

i2 : T_(0,2) = 9

o2 = 9

i3 : T

         ┌───┬───┬───┐
o3 =     │ 1 │ 9 │ 3 │
     ┌───┼───┼───┴───┘
     │ 4 │ 5 │        
     ├───┼───┘        
     │ 6 │            
     └───┘            

o3 : MutableYoungTableau