SkewTableau _ ZZ -- get the entries in a column.

Operator: _
Usage:

T_j
Inputs:
- T, an instance of the type SkewTableau, a tableau.
- j, an integer, the index of a column.
Outputs:
- l, a list, the entries in the $j$th column of T.

Description

Note that the resulting list may contain null entries in places where a box is not present. This means that the notations (T^i)#j, (T_j)#i, and T_(i,j) are all equivalent for valid positions (i,j). However, the notation T_(i,j) will raise an error for nonvalid positions, whereas the other two will return null.

i1 : T = skewTableau(new Partition from {4,3,1,0}, new Partition from {1,1}, {1,2,3,4,5,6})

         ┌───┬───┬───┐
o1 =     │ 1 │ 2 │ 3 │
         ├───┼───┼───┘
         │ 4 │ 5 │    
     ┌───┼───┴───┘    
     │ 6 │            
     └───┘            

o1 : SkewTableau

i2 : for i in columnRange T do print T_i
{, , 6}
{1, 4, }
{2, 5, }
{3, , }

i3 : (T^0)#1

o3 = 1

i4 : (T_1)#0

o4 = 1

i5 : T_(0,1)

o5 = 1

To get the column entries without extra null's, use columnEntries.

i6 : T'' = skewTableau(new Partition from {3,1}, new Partition from {-2,0,-1}, {1,2,3,4,5,6,7})

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

o6 : SkewTableau

i7 : T''_-1

o7 = {2, , 7}

o7 : List

i8 : columnEntries(T'',-1)

o8 = {2, 7}

o8 : List

Ways to use this method:

SkewTableau _ ZZ -- get the entries in a column.

The source of this document is in Tableaux/documentation.m2:520:0.

SkewTableau _ ZZ -- get the entries in a column.

Description

See also

Ways to use this method: