This paper is dedicated to the memory of J. Howard Redfield.

INTRODUCTION

Several years ago in a lecture at a British Mathematical Colloquium splinter group (Lancaster meeting, 1978) Dr. E.K. Lloyd mentioned that he had reason to believe that J. Howard Redfield had written a second (but unpublished) paper. As is well-known Redfield's first paper [17], published in 1927, was badly neglected although at least published. Attention as far as one knows was first drawn to it by Littlewood [13] in 1950. The paper was first publicized by Harary in 1960 [10]. It seemed that Redfield had anticipated most of the later discoveries in the theory of unlabelled enumeration such as Pólya's Hauptsatz, Read's Superposition Theorem, the counting of nonisomorphic graphs and the counting of self-complementary subsets of a set with respect to a group. At the end of 1981 I received an exciting letter from Lloyd stating that this second paper [18] had indeed been found. Apparently the paper had been submitted for publication in the American Journal of Mathematics on October 19th, 1940 and was rejected by the editors in a brief letter of January 7th, 1941. Harary and Robinson [12] have written a brief account of the circumstances leading up to the discovery of Redfield's second paper and happily a special edition of the Journal of Graph Theory is to be published entirely dedicated to Redfield.