numStandardTableaux -- compute the number of standard Young tableaux of a given shape

• Usage:

  numStandardTableaux lam

• Inputs:
  • lam, an instance of the type Partition, the shape, $\lambda$.
• Outputs:
  • n, an integer, the number of SYT of the given shape, and entries in $\{1,\ldots,N\}$, where $N$ is the number of boxes.

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

o1 = 35

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

o2 = 35