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We prove that for any k = 1, . . . , 2 the 2-adic order of the Stirling number S(2, k) of the second kind is exactly d(k) − 1, where d(k) denotes the number of 1’s among the binary digits of k. This confirms a conjecture of Lengyel.

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)

- Stefan De Wannemacker, Thomas Laffey, Robert Osburn
- J. Comb. Theory, Ser. A
- 2007

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)

- Davy Van Deursen, Igor Jacques, +5 authors Rik Van de Walle
- 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)

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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