conjugate(SkewTableau) -- conjugate a tableau

Function: conjugate
Usage:

conjugate T
Inputs:
- T, an instance of the type SkewTableau, a tableau.
Outputs:
- S, an instance of the type SkewTableau, the rows and columns have been switched.

Description

This method conjugates the tableau only if the shape has weakly decreasing parts, and no negative parts. Otherwise, it will raise an error.

i1 : T = skewTableau(new Partition from {6,6,5,3,1}, new Partition from {2,1,1}, toList(1..17))

               ┌────┬────┬────┬────┐
o1 =           │ 1  │ 2  │ 3  │ 4  │
          ┌────┼────┼────┼────┼────┤
          │ 5  │ 6  │ 7  │ 8  │ 9  │
          ├────┼────┼────┼────┼────┘
          │ 10 │ 11 │ 12 │ 13 │     
     ┌────┼────┼────┼────┴────┘     
     │ 14 │ 15 │ 16 │               
     ├────┼────┴────┘               
     │ 17 │                         
     └────┘                         

o1 : SkewTableau

i2 : conjugate T

                    ┌────┬────┐
o2 =                │ 14 │ 17 │
          ┌────┬────┼────┼────┘
          │ 5  │ 10 │ 15 │     
     ┌────┼────┼────┼────┤     
     │ 1  │ 6  │ 11 │ 16 │     
     ├────┼────┼────┼────┘     
     │ 2  │ 7  │ 12 │          
     ├────┼────┼────┤          
     │ 3  │ 8  │ 13 │          
     ├────┼────┼────┘          
     │ 4  │ 9  │               
     └────┴────┘               

o2 : SkewTableau

Ways to use this method:

conjugate(SkewTableau) -- conjugate a tableau

The source of this document is in Tableaux/documentation.m2:1003:0.