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Let n and k be natural numbers and let S(n, k) denote the Stirling numbers of the second kind. It is a conjecture of Wilf that the alternating sum n j=0 (−1) j S(n, j) is nonzero for all n > 2. We prove this conjecture for all n ≡ 2, 2944838 mod 3145728 and discuss applications of this result to graph theory, multiplicative partition functions , and the… (More)

With the term 'anti-monotonic function', we designate specific boolean functions on subsets of a finite set of positive integers which we call the universe. Through the well-known bijective relationship between the set of monotonic functions and the set of anti-monotonic functions , the study of the anti-monotonic functions is equivalent to the study of… (More)

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