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

Usage:

toIndex(T,seq)

toIndex(T,(i,j))

toIndex(seq,T)

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

Description

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

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 : thePosition = (1,2)

o2 = (1, 2)

o2 : Sequence

i3 : T_thePosition

o3 = 16

i4 : theIndex = toIndex(T,thePosition)

o4 = 6

i5 : (entries T)#theIndex

o5 = 16

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

i6 : skewTableau(new Partition from {6,3,2}, new Partition from {2}, toList(0..(size T - 1)))

             ┌───┬───┬───┬───┐
o6 =         │ 0 │ 1 │ 2 │ 3 │
     ┌───┬───┼───┼───┴───┴───┘
     │ 4 │ 5 │ 6 │            
     ├───┼───┼───┘            
     │ 7 │ 8 │                
     └───┴───┘                

o6 : SkewTableau

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

i7 : entryList = for i from 0 to size T - 1 list toPosition(T,i)

o7 = {(0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1)}

o7 : List

i8 : skewTableau(new Partition from {6,3,2}, new Partition from {2}, entryList)

                     ┌───────┬───────┬───────┬───────┐
o8 =                 │ (0,2) │ (0,3) │ (0,4) │ (0,5) │
     ┌───────┬───────┼───────┼───────┴───────┴───────┘
     │ (1,0) │ (1,1) │ (1,2) │                        
     ├───────┼───────┼───────┘                        
     │ (2,0) │ (2,1) │                                
     └───────┴───────┘                                

o8 : SkewTableau

Ways to use toIndex:

toIndex(Sequence,SkewTableau)
toIndex(SkewTableau,Sequence)

For the programmer

The object toIndex is a method function.

The source of this document is in Tableaux/documentation.m2:752:0.

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

Description

See also

Ways to use toIndex:

For the programmer