isCorner -- checks if a box is a corner of a tableau

Usage:

isCorner((rowIndex,colIndex), T)
Inputs:
- rowIndex, an integer, the row index of a box.
- colIndex, an integer, the column index of a box.
- T, an instance of the type YoungTableau, a Young tableau.
Outputs:
- b, a Boolean value, returns true if the box is a corner, and false otherwise.

Description

The corners of a tableau are the boxes that are both the last box in a row, and the last box in a column.

i1 : T = youngTableau(new Partition from {7,7,6,5,3,2,2,2,1}, new Partition from {3,1})

                 ┌───┬───┬───┬───┐
o1 =             │   │   │   │   │
         ┌───┬───┼───┼───┼───┼───┤
         │   │   │   │   │   │   │
     ┌───┼───┼───┼───┼───┼───┼───┘
     │   │   │   │   │   │   │    
     ├───┼───┼───┼───┼───┼───┘    
     │   │   │   │   │   │        
     ├───┼───┼───┼───┴───┘        
     │   │   │   │                
     ├───┼───┼───┘                
     │   │   │                    
     ├───┼───┤                    
     │   │   │                    
     ├───┼───┤                    
     │   │   │                    
     ├───┼───┘                    
     │   │                        
     └───┘                        

o1 : YoungTableau

i2 : isCorner((1,3),T)

o2 = false

i3 : applyPositions(T,thePosition -> isCorner(thePosition,T))

                             ┌───────┬───────┬───────┬───────┐
o3 =                         │ false │ false │ false │ false │
             ┌───────┬───────┼───────┼───────┼───────┼───────┤
             │ false │ false │ false │ false │ false │ true  │
     ┌───────┼───────┼───────┼───────┼───────┼───────┼───────┘
     │ false │ false │ false │ false │ false │ true  │        
     ├───────┼───────┼───────┼───────┼───────┼───────┘        
     │ false │ false │ false │ false │ true  │                
     ├───────┼───────┼───────┼───────┴───────┘                
     │ false │ false │ true  │                                
     ├───────┼───────┼───────┘                                
     │ false │ false │                                        
     ├───────┼───────┤                                        
     │ false │ false │                                        
     ├───────┼───────┤                                        
     │ false │ true  │                                        
     ├───────┼───────┘                                        
     │ true  │                                                
     └───────┘                                                

o3 : YoungTableau

Ways to use isCorner:

isCorner(Sequence,Partition)
isCorner(Sequence,YoungTableau)

For the programmer

The object isCorner is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Tableaux/documentation.m2:600:0.