Bart Kastermans

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Rational Generating Functions and Lattice Point Sets by<lb>Kevin M. Woods Chair: Alexander Barvinok We prove that, for any fixed d, there is a polynomial time algorithm for computing the<lb>generating function of any projection of the set of integer points in a d-dimensional<lb>polytope. This implies that many interesting sets of integer points can be(More)
Wemake progress toward solving a long-standing open problem in the area of computable linear orderings by showing that every computable η-like linear ordering without an infinite strongly η-like interval has a computable copy without nontrivial computable self-embedding. The precise characterization of those computable linear orderings which have computable(More)
It is an open problem in the area of computable randomness whether Kolmogorov-Loveland randomness coincides with Martin-Löf randomness. Joe Miller and André Nies suggested some variations of Kolmogorov-Loveland randomness to approach this problem and to provide a partial solution. We show that their proposed notion of partial permutation randomness is still(More)
If F ⊆ N N is an analytic family of pairwise eventually different functions then the following strong maximality condition fails: For any countable H ⊆ N N, no member of which is covered by finitely many functions from F , there is f ∈ F such that for all h ∈ H there are infinitely many integers k such that f (k) = h(k). However if V = L then there exists a(More)
Hirschfeldt and Shore have introduced a notion of stability for infinite posets. We define an arguably more natural notion called weak stability, and we study the existence of infinite computable or low chains or antichains, and of infinite Π1 chains and antichains, in infinite computable stable and weakly stable posets. For example, we extend a result of(More)
We consider the possible cardinalities of the following three cardinal invariants which are related to the permutation group on the set of natural numbers: ag := the least cardinal number of maximal cofinitary permutation groups; ap := the least cardinal number of maximal almost disjoint permutation families; c(Sym(N)) := the cofinality of the permutation(More)
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