This paper explores the potential of smart enumeration: enumeration of a design space giving the effect of exhaustive search, while using heuristics to order and reduce the search space. We characterise smart enumeration as having several key properties, including carefully chosen problem domains and techniques to speed up the search, such as those that exploit symmetry. Our approach has been a...

In this paper we propose a hybrid algorithm for the set covering problem (SCP), which combines L-class enumeration, genetic algorithm (GA) and Lagrangean heuristic. The lexicographical enumeration of L-classes in the linear relaxation of SCP ensures optimality of the resulting solution. Both heuristics are used for obtaining the initial approximate solution. The linear subproblems in L-class en...

In this paper we describe numeric as well as symbolic algorithms for the enumeration of substitutional isomers with an unlimited number of different achiral substituents. We consider three different scenarios: first, the enumeration of diamutamers with a given set of ligand types and ligand multiplicity, second, the enumeration of diamutamer libraries with a given ligand assortment pattern, and...

We obtain a new expression for the partition function of the 8VSOS model with domain wall boundary conditions, which we consider to be the natural extension of the Izergin– Korepin formula for the six-vertex model. As applications, we find dynamical (in the sense of the dynamical Yang–Baxter equation) generalizations of the enumeration and 2-enumeration of alternating sign matrices. The dynamic...

We combine the parametric Barvinok algorithm with a generation algorithm for a finite list of suitably chosen discrete sub-cases on the enumeration of complete simple games, i. e. a special subclass of monotone Boolean functions. Recently, Freixas et al. have proven an enumeration formula for complete simple games with two types of voters. We will provide a shorter proof and an enumeration form...

The abilities to enumerate small sets of items (e.g., dots) and to compare magnitudes are claimed to be indexes of core numerical competences that scaffold early math development. Insofar as this is correct, these abilities may be diagnostic markers of math competence in preschoolers. However, unlike magnitude comparison abilities, little research has examined preschoolers' ability to enumerate...