FIGURE 10.
Effect of increasing the size or dimension of the problem. Starting with the case where z = 3 and m = 2, incrementing z to get D(4,2) is equivalent to adding D(4,1); In other words, the next larger case in one less dimension (top). Conversely, incrementing m to get D(3,3) is equivalent to adding D(2,2) and D(1,2) (side: left of arrow). This is equivalent to adding D(2,3) (because a given term in d dimensions is the same as the sum of all terms up to that size in d − 1 dimensions as shown in Fig. 9); in other words, this is the same as adding the next smaller case in the same number of dimensions (side: right of arrow).
