skewShape -- the shape of a skew tableau

Usage:

(lam,mu) = skewShape T
Inputs:
- T, an instance of the type SkewTableau, a skew tableau.
Outputs:
- lam, an instance of the type Partition, the outer shape, $\lambda$, of T.
- mu, an instance of the type Partition, the inner shape, $\mu$, of T.

Description

This returns the original shape used to construct the tableau.

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

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

o1 : SkewTableau

i2 : skewShape T

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

o2 : Sequence

It may be convenient to remove trailing $0$'s from the partitions by using truncate on a sequence of two partitions.

i3 : truncate skewShape T

o3 = (Partition{4, 3, 1}, Partition{2, 1})

o3 : Sequence

It may also be useful to append $0$s to make the partitions have the same number of parts.

i4 : (lam',mu') = pad skewShape T

o4 = (Partition{4, 3, 1, 0}, Partition{2, 1, 0, 0})

o4 : Sequence

i5 : rowLengths' = for i from 0 to #lam'-1 list(lam'#i-mu'#i)

o5 = {2, 2, 1, 0}

o5 : List

You may also 'standardize' a skew shape to return a pair of partitions of equal length, without extra $0$'s. I.e., one of the resulting partitions will end with a nonzero part, and the other will be padded with $0$'s.

i6 : (lam'',mu'') = standardize skewShape T

o6 = (Partition{4, 3, 1}, Partition{2, 1, 0})

o6 : Sequence

i7 : rowLengths = for i from 0 to #lam''-1 list(lam''#i-mu''#i)

o7 = {2, 2, 1}

o7 : List

Ways to use skewShape:

skewShape(SkewTableau)

For the programmer

The object skewShape is a method function.

The source of this document is in Tableaux/documentation.m2:305:0.

skewShape -- the shape of a skew tableau

Description

See also

Ways to use skewShape:

For the programmer