On the effective and automatic enumeration of polynomial permutation classes

We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations of length n which can be obtained by a finite number of block sorting operations (e.g., reversals, block transpositions, cut-and-paste moves)

A collaborative ant colony metaheuristic for distributed multi-level lot-sizing

The paper presents an ant colony optimization metaheuristic for collaborative planning. Collaborative planning is used to coordinate individual plans of self-interested decision makers with private information in order to increase the overall benefit of the coalition. The method consists of a new search graph based on encoded solutions. Distributed and private information is integrated via voting mechanisms and via a simple but effective collaborative local search procedure. The approach is applied to a distributed variant of the multi-level lot-sizing problem and evaluated by means of 352 benchmark instances from the literature. The proposed approach clearly outperforms existing approaches on the sets of medium and large sized instances. While the best method in the literature so far achieves an average deviation from the best known non-distributed solutions of 46 percent for the set of the largest instances, for example, the presented approach reduces the average deviation to only 5 percent

Generating Permutations with Restricted Containers

We investigate a generalization of stacks that we call $\mathcal{C}$-machines. We show how this viewpoint rapidly leads to functional equations for the classes of permutations that $\mathcal{C}$-machines generate, and how these systems of functional equations can frequently be solved by either the kernel method or, much more easily, by guessing and checking. General results about the rationality, algebraicity, and the existence of Wilfian formulas for some classes generated by $\mathcal{C}$-machines are given. We also draw attention to some relatively small permutation classes which, although we can generate thousands of terms of their enumerations, seem to not have D-finite generating functions

Pattern-Avoiding Involutions: Exact and Asymptotic Enumeration

We consider the enumeration of pattern-avoiding involutions, focusing in particular on sets defined by avoiding a single pattern of length 4. As we demonstrate, the numerical data for these problems demonstrates some surprising behavior. This strange behavior even provides some very unexpected data related to the number of 1324-avoiding permutations

On the medical history of the doctrine of imagination

In the early moderera the notion of imagination was made responsible for phenomena which were later explained in terms of embryology, genetics, psychology, bacteriology or other scientific disciplines. Images, often seated in the upper abdomen (hypochondriac region) or the womb (hysteria), were regarded as powerful influences on material reality. In the course of the seventeenth and eighteenth centuries the hypochondriac forms of imagination became mere whims and spleens, but they kept much of their original potency in respect of the uterus, accounting for monstrosities and the shaping of human offspring. The hysterical conversion of imagination into somatic phenomena has never been questioned. Since the two World Wars the realm of imagination has again expanded beyond the uterus and the older disease-concepts. In the last 10-20 years images seem to have regained some of their original creative forc