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On the number of monotonic functions from two-valued logic to k-valued logic

The problem of number determination of monotonic functions of n variables-i^(n) was formulated and solved for n = 4 by Dedekind [3] in 1897. For n = 5 and n = 6, this problem was solved in Church [2] and in Ward [12] respectively. The further authors bringing the essential improvement of the estimates of \j/(n) were Gilbert [4], Korobkov [8, 9, 10], Hansel [5], and Kleitman [7] who gave an asymptotic estimate of log2 iji(n). The best known result obtained is Korshunov's asymptotic estimate (*)of^(n)(of[ll])