tabloid -- constructor for type Tabloid

• Usage:

  tabloid(lam, mu, entryList)

  tabloid((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.
• Outputs:
  • T, an instance of the type Tabloid, a tabloid of shape $\lambda/\mu$ with the given 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 $3$.
  • The entries are $\{1,\ldots,N\}$, where $N$ is the number of boxes.

i1 : lam = new Partition from {4,3,2}

o1 = Partition{4, 3, 2}

o1 : Partition

i2 : mu = new Partition from {3,1}

o2 = Partition{3, 1}

o2 : Partition

i3 : entryList = {1,4,2,3,5}

o3 = {1, 4, 2, 3, 5}

o3 : List

i4 : T = tabloid(lam,mu,entryList)

                 ┌───┐
o4 =             │ 1 │
         ┌───────┼───┘
         │ 4   2 │    
     ┌───┴───┬───┘    
     │ 3   5 │        
     └───────┘        

o4 : Tabloid