The first four boundary curves are given by: 0 = b − a, (82) 0 = 3 ab − b + a 2 + a, (83) 0 = 3 ab 2 − b 2 + 2 ba 2 + 6 ab − a 3 − a $^{2}$, (84) 0 = 5 a $^{2}$b2 − 10 ab 2 + b 2 + 6 ba 3 − 6 ab + a 4 + 2 a 3 + a $^{2}$. (85) These curves are, respectively, linear, quadratic, cubic, and quartic. Because the (32) n and (2)(32) n processes share boundary curves, the allowed regions are contiguous and non- overlapping. Furthermore, the asymptotes, having the basic form a = tan $^{2}$( π/ (2(2 m + 1))) , approach a = 0 in the limit as n approaches ∞ , and so the entire a − b plane above the line b = a is covered by allowed regions for processes of these types. The allowed regions for (32), (232), and (3232) are given in figure 3. FIG. 3: The pairs of curves which, going from right to left, give the allowed regions for (32), (232), (3232) and higher order processes. 23