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

TL;DR

This survey reviews the 40-year collaborative work of Goulden and Jackson, highlighting their contributions to combinatorial enumeration, symmetric functions, permutation factorizations, and algebraic foundations across various scientific fields.

Contribution

It summarizes their groundbreaking research, textbooks, and influence across disciplines, emphasizing their novel approaches in combinatorial and algebraic enumeration.

Findings

Significant advances in permutation factorizations

Development of algebraic methods in quantum field theory

Influence on bioinformatics and mathematical chemistry

Abstract

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, {\em 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.