SOME COMBINATORIAL RESULTS FIRST FOUND USING COMPUTER ALGEBRA

The goal of this paper is to present a panorama of some recent combina torial results that we first discovered through experimentation with s ymbolic computation software. Each statement presented here has been r igorously 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. The se 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 combinator ial structures, and the limiting fraction of the nodes having given pr operties in large random quadtrees. (C) 1995 Academic Press Limited