Enumerative and Algebraic Combinatorics in the 1960’s and 1970’s

Abstract

The period 1960–1979 was an exciting time for enumerative and algebraic combinatorics (EAC). During this period EAC was transformed into an independent subject which is even stronger and more active today. I will not attempt a comprehensive analysis of the development of EAC but rather focus on persons and topics that were relevant to my own career. Thus the discussion will be partly autobiographical. There were certainly deep and important results in EAC before 1960. Work related to tree enumeration (including the Matrix-Tree theorem), partitions of integers (in particular, the Rogers-Ramanujan identities), the Redfield-Pólya theory of enumeration under group action, and especially the representation theory of the symmetric group, GL(n,C) and some related groups, featuring work by Georg Frobenius (1849–1917), Alfred Young (1873–1940), and Issai Schur (1875–1941), are some highlights. Much of this work was not concerned with combinatorics per se; rather, combinatorics was the natural context for its development. For readers interested in the development of EAC, as well as combinatorics in general, prior to 1960, see Biggs [14], Knuth [77, §7.2.1.7], Stein [147], and Wilson and Watkins [153]. Before 1960 there are just a handful of mathematicians who did a substantial amount of enumerative combinatorics. The most important and influential of these is Percy Alexander MacMahon (1854–1929). He was a highly original pioneer, whose work was not properly appreciated during his lifetime except for his contributions to invariant theory and integer partitions. Much of the work in EAC in the