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

Usage:

positionList T

positionList(T,f)
Inputs:
- T, an instance of the type YoungTableau, a tableau.
- f, a function, a function that acts on the positions, and returns either true or false.
Outputs:
- l, a list, the positions (i,j) of boxes in T. If a function f is provided, then only the positions returning true are in the list.

Description

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

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

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

o1 : YoungTableau

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' = youngTableau(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 : YoungTableau

Including a function returns only the positions that return true. For example, the following code returns all positions of corners in the tableau, using function isCorner.

i4 : positionList(T, thePosition -> isCorner(thePosition,T))

o4 = {(0, 5), (1, 2), (2, 1)}

o4 : List

Ways to use positionList:

positionList(YoungTableau)
positionList(YoungTableau,Function)

For the programmer

The object positionList is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Tableaux/documentation.m2:937:0.

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

Description

See also

Ways to use positionList:

For the programmer