numTabloids -- compute the number of tabloids of a given shape

• Usage:

  numTabloids(lam,mu)

• Inputs:
  • lam, an instance of the type Partition, the outer shape $\lambda$.
  • mu, an instance of the type Partition, the inner shape $\mu$. If not given, then it is assumed to be the $0$ partition.
• Outputs:
  • n, an integer, the number of tabloids of the given shape, and entries in $\{1,\ldots,N\}$, where $N$ is the number of boxes.

i1 : # allTabloids(new Partition from {4,2,1})

o1 = 105

i2 : numTabloids(new Partition from {4,2,1})

o2 = 105