Combinatorial and Algebraic Enumeration: a survey of the work of Ian P. Goulden and David M. Jackson

In this survey we discuss some of the significant contributions of Ian Goulden and David Jackson in the areas of classical enumeration, symmetric functions, factorizations of permutations, and algebraic foundations of quantum field theory. Through their groundbreaking textbook, Combinatorial Enumeration, and their numerous research papers, both together and with their many students, they have had an influence in areas of bioinformatics, mathematical chemistry, algorithmic computer science, and theoretical physics. Here we review and set in context highlights of their 40 years of collaborative work. Separately—but most notably together—Ian Goulden and David Jackson have made a major impact in the fields of algebraic and combinatorial enumeration. Their contributions run the gamut from writing a groundbreaking textbook and authoritative reference, to co-founding a well-regarded journal, to publishing over 50 research papers together in their collaboration lasting over 40 years. This survey article explores some of their key results.