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)
In loving memory of my father I would like to express my thanks to my supervisor David Lewis for giving me the opportunity to do my doctorate at the University College Dublin and for his belief in my ability. I would also like to thank Jean-Pierre Tignol, Jan Van Geel and Anne Cortella for the many insightful discussions on various topics covered in this(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)
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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