numSemistandardTableaux -- compute the number of semistandard Young tableaux of a given shape

• Usage:

  numSemistandardTableaux(lam,N)

• Inputs:
  • lam, an instance of the type Partition, the shape, $\lambda$.
  • N, an integer, the maximum entry.
• Outputs:
  • n, an integer, the number of SSYT of the given shape, and entries in 1..N. If N is not provided, it is assumed to be the length of the shape.

i1 : # allSemistandardTableaux(new Partition from {6,6,5,1,1})

o1 = 2520

i2 : numSemistandardTableaux(new Partition from {6,6,5,1,1})

o2 = 2520