Stefan De Wannemacker

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We present a set of generators of the full annihilator ideal for the Witt ring of an arbitrary field of characteristic unequal to two satisfying a non-vanishing condition on the powers of the fundamental ideal in the torsion part of the Witt ring. This settles a conjecture of Ongenae and Van Geel. This result could only be proved by first obtaining a new(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)S(n, j) is nonzero for all n > 2. We prove this conjecture for all n 6≡ 2, 2944838 mod 3145728 and discuss applications of this result to graph theory, multiplicative partition functions, and the(More)
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)
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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