SkewTableau ^ ZZ -- get the entries in a row.

Operator: ^
Usage:

T^i
Inputs:
- T, an instance of the type SkewTableau, a tableau.
- i, an integer, the index of a row.
Outputs:
- l, a list, the entries in the $i$th row 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 from 0 to numRows T - 1 do print T^i
{, 1, 2, 3}
{, 4, 5, }
{6, , , }

i3 : (T^0)#1

o3 = 1

i4 : (T_1)#0

o4 = 1

i5 : T_(0,1)

o5 = 1

If T has negative rows, then the entries at negative column coordinates are to the right in the output.

i6 : T' = skewTableau(new Partition from {4,3,1,0}, new Partition from {1,-1}, {1,2,3,4,5,6,7,8})

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

o6 : SkewTableau

i7 : for i from 0 to numRows T' - 1 do print T'^i
{, 1, 2, 3, }
{5, 6, 7, , 4}
{8, , , , }

i8 : T'^1#-1

o8 = 4

i9 : T'_(1,-1)

o9 = 4

To get the row entries exactly as they appear in the tableau and without extra null's, use rowEntries.

i10 : T'' = skewTableau(new Partition from {3,4}, new Partition from {-2}, {1,2,3,4,5,6,7,8,9})

      ┌───┬───║───┬───┬───┐    
o10 = │ 1 │ 2 ║ 3 │ 4 │ 5 │    
      └───┴───║───┼───┼───┼───┐
              ║ 6 │ 7 │ 8 │ 9 │
              ║───┴───┴───┴───┘

o10 : SkewTableau

i11 : T''^0

o11 = {3, 4, 5, , 1, 2}

o11 : List

i12 : rowEntries(T'',0)

o12 = {1, 2, 3, 4, 5}

o12 : List

Ways to use this method:

SkewTableau ^ ZZ -- get the entries in a row.

The source of this document is in Tableaux/documentation.m2:481:0.

SkewTableau ^ ZZ -- get the entries in a row.

Description

See also

Ways to use this method: