Constructing certain combinatorial structures by computational methods
Harri Haanpää · Aaltodoc (Aalto University) · 2004
Combinatorics is a branch of mathematics that generally deals with a finite or at most countably infinite set and collections of its subsets. These collections must then satisfy certain criteria depending on the class of objects and the problem being considered. The most fundamental problem in combinatorics is the problem of existence: Does a combinatorial structure that satisfies the given requirements exist? In general, it is straightforward to verify that a proposed structure satisfies the required criteria, but finding a structure of the required type is difficult. If a structure of the required type exists, any method that constructs one is sufficient to settle the existence question. Two problems closely related to the existence problem are the enumeration problem—how many different combinatorial structures of the required type exist—and the optimization problem—which combinatorial structure of the required type is the best, judged by some criterion. A computer may