Gian-Carlo Rota on combinatorics

In this volume, the editor, Joseph Kung, presents reprints of most of the fundamental papers of Gian-Carlo Rota in the classical core of combinatorics. These include Part I, III, IV, VI, and VII of the Foundation series on Mobius function, polynomials of binomial type, counting in vector spaces, generating functions, and symmetric functions. Also reprinted are papers which are derived or related to the themes explored in these central papers. Rota's work, starting with the paper On the Foundations of Combinatorial Theory I. Theory of Mobius Functions (1964) has revolutionized the way we approach combinatorics; this volume is intended to be an introduction to his way of thinking about that subject. Joseph Kung has provided us with a substantial amount of new material on the tremendous impact that Rota's papers have had on combinatorics. Extensive survey articles are included in every chapter to guide the reader, both to the reprinted papers and to the works of others which have been inspired by these papers. And, there are four prefatory essays describing Rota's special influence on combinatorics, particularly at the historical Bowdoin conference in 1970. . This volume will be of interest to experts as well as beginning graduate students (particularly as a source of research problems).