May 5 2000

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THEOREM 2^*). For any m ³ 1 and r ³ 2,

IF $ n*(m,r) Q(n*(m,r)), where Q = a) & b) & c) and

a) n^*(m,r) = , n_i ³ m,

b) for all s = s₀ , s₀ + 1, s₀ + 2 , ... , s₁ ,

c) s₁ - s₀ ³ g(m-1, r),

THEN " n > n₀(m,r) P(n), where

P(n) = " n = , n_{i ³} m, s^* = g(m-1,r) + s₀ ,

so that G(m,r) £ g(m-1,r) + s₀ , and

n₀(m,r) = n*(m,r) + (g(m-1,r) + s₀ )× (m-1)^r + ,

= max { Z(m-1,r) }.