Niceness theorems

Many things in mathematics seem lamost unreasonably nice. This includes objects, counterexamples, proofs. In this preprint I discuss many examples of this phenomenon with emphasis on the ring of polynomials in a countably infinite number of variables in its many incarnations such as the representing object of the Witt vectors, the direct sum of the rings of representations of the symmetric groups, the free lambda ring on one generator, the homology and cohomology of the classifying space BU, ... . In addition attention is paid to the phenomenon that solutions to universal problems (adjoint functors) tend to pick up extra structure.Comment: 52 page

Comparative Evaluation of Packet Classification Algorithms for Implementation on Resource Constrained Systems

This paper provides a comparative evaluation of a number of known classification algorithms that have been considered for both software and hardware implementation. Differently from other sources, the comparison has been carried out on implementations based on the same principles and design choices. Performance measurements are obtained by feeding the implemented classifiers with various traffic traces in the same test scenario. The comparison also takes into account implementation feasibility of the considered algorithms in resource constrained systems (e.g. embedded processors on special purpose network platforms). In particular, the comparison focuses on achieving a good compromise between performance, memory usage, flexibility and code portability to different target platforms

Phase transitions related to the pigeonhole principle

Since Paris introduced them in the late seventies (Paris1978), densities turned out to be useful for studying independence results. Motivated by their simplicity and surprising strength we investigate the combinatorial complexity of two such densities which are strongly related to the pigeonhole principle. The aim is to miniaturise Ramsey's Theorem for $1$-tuples. The first principle uses an unlimited amount of colours, whereas the second has a fixed number of two colours. We show that these principles give rise to Ackermannian growth. After parameterising these statements with respect to a function f:N->N, we investigate for which functions f Ackermannian growth is still preserved