January 2008
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43 Reads
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6 Citations
Say an integer n is exceptional if the maximum Stirling number of the second kind S(n,k) occurs for two (of necessity consecutive) values of k. We prove that the number of exceptional integers less than or equal to x is O(x 1/2+ε ), for any ε>0. We derive a similar result for partitions of n into exactly k integers.