isWeaklyDecreasing -- check if shapes are weakly decreasing

• Usage:

  isWeaklyDecreasing T

  isWeaklyDecreasing (lam,mu)

  isWeaklyDecreasing lam

• Inputs:
  • T, an instance of the type YoungTableau, a tableau.
  • lam, an instance of the type Partition, the outer shape, $\lambda$.
  • mu, an instance of the type Partition, the inner shape, $\mu$.
• Outputs:
  • b, a Boolean value, returns true if both shapes have weakly decreasing parts, and false otherwise.

i1 : isWeaklyDecreasing youngTableau(new Partition from {6,6,5,3,1}, new Partition from {2,1,1})

o1 = true

i2 : isWeaklyDecreasing new Partition from {5,3,-1,0}

o2 = false