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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)

- Davy Van Deursen, Igor Jacques, Stefan De Wannemacker, Steven Torrelle, Wim Van Lancker, Maribel Montero Perez +2 others
- 2011

The possibilities within e-learning environments increased dramatically the last couple of years. They are more and more deployed on the Web, allow various types of tasks and fine-grained feedback, and they can make use of audiovisual material. On the other hand, we are confronted with an increasing heterogeneity in terms of end-user devices (smartphones,… (More)

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)

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