boxContent -- compute the content of a box of a tableau

Usage:

boxContent(i,j)
Inputs:
- i, an integer, the row index of a box.
- j, an integer, the column index of a box.
Outputs:
- n, an integer, the hook length of box (i,j).

Description

The content of box (i,j) is defined as $j-i$.

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

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

o1 : YoungTableau

i2 : boxContent(1,1)

o2 = 0

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

               ┌────┬────┬────┬────┐
o3 =           │ 2  │ 3  │ 4  │ 5  │
          ┌────┼────┼────┼────┼────┤
          │ 0  │ 1  │ 2  │ 3  │ 4  │
          ├────┼────┼────┼────┼────┘
          │ -1 │ 0  │ 1  │ 2  │     
     ┌────┼────┼────┼────┴────┘     
     │ -3 │ -2 │ -1 │               
     ├────┼────┴────┘               
     │ -4 │                         
     └────┘                         

o3 : YoungTableau

Ways to use boxContent:

boxContent(ZZ,ZZ)

For the programmer

The object boxContent is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Tableaux/documentation.m2:303:0.