toPosition -- get the position of a box, given its index.

Usage:

toPosition(T,k)

toPosition(k,T)
Inputs:
- T, an instance of the type SkewTableau, a tableau.
- k, an integer, the index of a box.
Outputs:
- l, a sequence, the position (i,j) of the box in T.

Description

The boxes in entries T fill the tableau from top to bottom, and left to right. Hence, an index in entries T corresponds to a position (i,j).

i1 : T = skewTableau(new Partition from {6,3,2}, new Partition from {2}, toList(10..18))

               ┌────┬────┬────┬────┐
o1 =           │ 10 │ 11 │ 12 │ 13 │
     ┌────┬────┼────┼────┴────┴────┘
     │ 14 │ 15 │ 16 │               
     ├────┼────┼────┘               
     │ 17 │ 18 │                    
     └────┴────┘                    

o1 : SkewTableau

i2 : (entries T)#5

o2 = 15

i3 : toPosition(T,5)

o3 = (1, 1)

o3 : Sequence

We may replace the filling in each box with its index to see the order.

i4 : skewTableau(new Partition from {6,3,2}, new Partition from {2}, toList(0..(size T - 1)))

             ┌───┬───┬───┬───┐
o4 =         │ 0 │ 1 │ 2 │ 3 │
     ┌───┬───┼───┼───┴───┴───┘
     │ 4 │ 5 │ 6 │            
     ├───┼───┼───┘            
     │ 7 │ 8 │                
     └───┴───┘                

o4 : SkewTableau

We may also replace the filling in each box with the corresponding position.

i5 : entryList = for i from 0 to size T - 1 list toPosition(T,i)

o5 = {(0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1)}

o5 : List

i6 : skewTableau(new Partition from {6,3,2}, new Partition from {2}, entryList)

                     ┌───────┬───────┬───────┬───────┐
o6 =                 │ (0,2) │ (0,3) │ (0,4) │ (0,5) │
     ┌───────┬───────┼───────┼───────┴───────┴───────┘
     │ (1,0) │ (1,1) │ (1,2) │                        
     ├───────┼───────┼───────┘                        
     │ (2,0) │ (2,1) │                                
     └───────┴───────┘                                

o6 : SkewTableau

Ways to use toPosition:

toPosition(SkewTableau,ZZ)
toPosition(ZZ,SkewTableau)

For the programmer

The object toPosition is a method function.

The source of this document is in Tableaux/documentation.m2:707:0.

toPosition -- get the position of a box, given its index.

Description

See also

Ways to use toPosition:

For the programmer