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positionList -- get the positions of all the boxes in a tableau

Description

This method is useful for iterating over all positions in a tableau

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 : theList = positionList T

o2 = {(0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1)}

o2 : List
 
i3 : T' = skewTableau(new Partition from {6,3,2}, new Partition from {2}, theList)

                     ┌───────┬───────┬───────┬───────┐
o3 =                 │ (0,2) │ (0,3) │ (0,4) │ (0,5) │
     ┌───────┬───────┼───────┼───────┴───────┴───────┘
     │ (1,0) │ (1,1) │ (1,2) │                        
     ├───────┼───────┼───────┘                        
     │ (2,0) │ (2,1) │                                
     └───────┴───────┘                                

o3 : SkewTableau

See also

Ways to use positionList:

  • positionList(SkewTableau)

For the programmer

The object positionList is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Tableaux/documentation.m2:778:0.