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columnRange -- the range of column indices of a tableau.

Description

Although it is straightforward that the row indices are 0..(numRows T - 1), the analogous sequence does not work for columns since columns may have negative indices. Hence, columnRange provides an easy way to iterate over column indices. The lowest number is the smallest part of the tableau's shape, and the largest number is the largest part of its shape.

i1 : T = skewTableau(new Partition from {8,7,6,6,1}, new Partition from {4,4,3,2,-2}, toList(1..17))

               ║                   ┌────┬────┬────┬────┐
o1 =           ║                   │ 1  │ 2  │ 3  │ 4  │
               ║                   ├────┼────┼────┼────┘
               ║                   │ 5  │ 6  │ 7  │     
               ║              ┌────┼────┼────┼────┘     
               ║              │ 8  │ 9  │ 10 │          
               ║         ┌────┼────┼────┼────┤          
               ║         │ 11 │ 12 │ 13 │ 14 │          
     ┌────┬────║────┐    └────┴────┴────┴────┘          
     │ 15 │ 16 ║ 17 │                                   
     └────┴────║────┘                                   

o1 : SkewTableau
 
i2 : columnRange T

o2 = (-2, -1, 0, 1, 2, 3, 4, 5, 6, 7)

o2 : Sequence
 
i3 : for j in columnRange T do print columnEntries(T,j)
{15}
{16}
{17}
{}
{11}
{8, 12}
{1, 5, 9, 13}
{2, 6, 10, 14}
{3, 7}
{4}

See also

Ways to use columnRange:

  • columnRange(SkewTableau)

For the programmer

The object columnRange is a method function.

The source of this document is in Tableaux/documentation.m2:581:0.