standardize -- standardize the lengths of a pair of partitions

• Usage:

  (lam',mu') = standardize (lam,mu)

• Inputs:
  • lam, an instance of the type Partition, a partition.
  • mu, an instance of the type Partition, a partition.
• Outputs:
  • lam', an instance of the type Partition, a partition obtained from lam, with trailing zeros added or removed.
  • mu', an instance of the type Partition, a partition obtained from mu, with trailing zeros added or removed.
• Consequences:

  • Partitions lam' and mu' have the same number of parts, possibly with trailing 0s.

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

             ┌───┬───┐
o1 =         │   │   │
         ┌───┼───┼───┘
         │   │   │    
     ┌───┼───┴───┘    
     │   │            
     └───┘            

o1 : YoungTableau

i2 : skewShape T

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

o2 : Sequence

i3 : standardize skewShape T

o3 = (Partition{4, 3, 1}, Partition{2, 1, 0})

o3 : Sequence