hookLength -- compute the hook length of a box of a tableau

Usage:

hookLength(thePosition,T)
Inputs:
- thePosition, a sequence, a pair (i,j) of integers.
- T, an instance of the type SkewTableau, a tableau.
Outputs:
- n, an integer, the hook length of box (i,j) in T.

Description

The hook length of box (i,j) is defined as the number of boxes directly below, and directly to the right, of a box, including the box itself.

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

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

o1 : SkewTableau

i2 : hookLength((1,1),T)

o2 = 7

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

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

o3 : SkewTableau

Ways to use hookLength:

hookLength(Sequence,SkewTableau)

For the programmer

The object hookLength is a method function.

The source of this document is in Tableaux/documentation.m2:1029:0.