youngTableau -- constructor for type YoungTableau

Usage:

youngTableau(lam, entryList)
Inputs:
- lam, an instance of the type Partition, the shape $\lambda$.
- 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 YoungTableau, a (nonskew) Young tableau of shape $\lambda$ with the given filling.
Consequences:
- The list of entries has length equal to $\sum_{i=1}^{\ell(\lambda)}|\lambda_i|$. E.g., if $\lambda=(-2)$, then the entry list must have length $2$.
- None of the entries are null.

Description

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

o1 = Partition{4, 3, 2}

o1 : Partition

i2 : entryList = {1,2,3,4,5,6,7,8,9}

o2 = {1, 2, 3, 4, 5, 6, 7, 8, 9}

o2 : List

i3 : T = youngTableau(lam,entryList)

     ┌───┬───┬───┬───┐
o3 = │ 1 │ 2 │ 3 │ 4 │
     ├───┼───┼───┼───┘
     │ 5 │ 6 │ 7 │    
     ├───┼───┼───┘    
     │ 8 │ 9 │        
     └───┴───┘        

o3 : YoungTableau

We may construct tableaux with any compositions.

i4 : youngTableau(new Partition from {3,5,1}, {7,"&",4,2,"g","u",6,0,-1})

     ┌────┬────┬────┐          
o4 = │ 7  │ &  │ 4  │          
     ├────┼────┼────┼────┬────┐
     │ 2  │ g  │ u  │ 6  │ 0  │
     ├────┼────┴────┴────┴────┘
     │ -1 │                    
     └────┘                    

o4 : YoungTableau

The shape may have negative parts. In this case, a vertical line is drawn by net to indicate that negative parts are to the left. If any $\lambda_i<0$, then the boxes in that row are drawn shaded.

i5 : youngTableau(new Partition from {-2,-4,2})

             ┌───┬───║        
o5 =         │░░░│░░░║        
     ┌───┬───┼───┼───║        
     │░░░│░░░│░░░│░░░║        
     └───┴───┴───┴───║───┬───┐
                     ║   │   │
                     ║───┴───┘

o5 : YoungTableau

We may cast an object of type YoungTableau to type SkewTableau.

i6 : T' = youngTableau(new Partition from {3,1,1})

     ┌───┬───┬───┐
o6 = │   │   │   │
     ├───┼───┴───┘
     │   │        
     ├───┤        
     │   │        
     └───┘        

o6 : YoungTableau

i7 : skewTableau T'

     ┌───┬───┬───┐
o7 = │   │   │   │
     ├───┼───┴───┘
     │   │        
     ├───┤        
     │   │        
     └───┘        

o7 : SkewTableau

Ways to use youngTableau:

youngTableau(Partition)
youngTableau(Partition,List)

For the programmer

The object youngTableau is a method function.

The source of this document is in Tableaux/documentation.m2:172:0.

youngTableau -- constructor for type YoungTableau

Description

See also

Ways to use youngTableau:

For the programmer