L-R Rule

The Littlewood-Richardson coefficients $c^\nu_{\lambda,\mu}$ describe the product of Schur functions. The following is an example of computing $c^\nu_{\lambda,\mu}$ using the rule described in this paper by J. B. Remmel and R. Whitney. The coefficient is equal to the number of tableaux of shape $\nu$ which can be created by adding boxes in the blue-shaded positions subject to the following rules:
  1. If $x$ and $x+1$ occur in the same row of the skew tableau on the left, then $x+1$ must occur in a cell weakly above and strictly to the right of the cell in which $x$ occurs in the tableau being created
  2. If $y$ occurs in the same column and in a row immediately below where $x$ occurs in the tableau on the left, then $y$ must occur in a cell which is strictly below and weakly to the left of $x$
Try different shapes for $\lambda$ and $\mu$: