Some Combinatorial Results First Found Using Computer Algebra

The goal of this paper is to present a panorama of some recent combinatorial results that we first discovered through experimentation with symbolic computation software. Each statement presented here has been rigorously proved using standard methods. Emphasis is laid on the (self-contained) description of the context as well as on the methods that were used to find the results in the first place, using computers. These include examples, counter-examples, and properties of combinatorial cycle index and asymmetry index series subject to certain constraints, the study of canonical q-series associated to families of combinatorial structures, and the limiting fraction of the nodes having given properties in large random quadtrees.