Studies in Combinatorics: 17

Combinatorics has recently awakened from a long slumber, which began at the time of Euler. It has emerged as a new subject standing at the crossroads between pure and applied mathematics, the center of bustling activity, a simmering pot of new problems and exciting speculations.The seven papers of this survey represent a wide enough sampling of current trends, from which the reader may, at least, extrapolate some of the missing material. They bear in common the one characteristic of contemporary combinatorics: striving for general new results, while using old and new problems as a test of efficiency.The introduction to matroid theory by Brylawski and Kelly describes a theory whose background — at least from a distance — is the four-color conjecture, much like the background of algebraic number theory was, at least at the beginning, Fermat's conjecture. It matters little that neither theory has succeeded in solving its motivating problem...