Wilson Co-Authors Second Edition of Research Monograph

The second edition of the research monograph, “Analytic Combinatorics in Several Variables,” written by Manning College of Information and Computer Sciences Senior Teaching Faculty member Mark C. Wilson, Robin Pemantle of the University of Pennsylvania, and Stephen Melczer of the University of Waterloo, was published by Cambridge University Press on February 15. 

The result of 25 years’ work, the “vastly improved” new edition provides a more accessible and user-friendly approach to understanding and deploying analytic combinatorics in several variables (ACSV), a concept created by Wilson and Pemantle. 

“Analytic combinatorics deals with using a mathematical subfield called complex analysis to approximately compute the number or probability of structures of large size,” says Wilson. “It has been heavily used in the analysis of algorithms, queuing theory, and information theory, in particular. ACSV deals with this in several variables, where more refined questions can be asked—not just how big an object is, but more detailed questions such as the number of occurrences of a given pattern, for example.” 

The revised book contains additional exercises and computational examples utilizing Sage worksheets to illustrate the main results, with updated background material and a new chapter providing a conceptual overview. To date, the methodology presented by Wilson, Pemantle, and Melczer has been applied to models in physics—string theory, quantum gravity, and statistical mechanics—as well as coding and information theory and in models of polymers and RNA. 

“We hope our work will continue to have broad application and inspire a new generation of researchers to enter the field, which combines beauty, utility, and tractability in a way that is rare in our experience,” says Wilson. 

Wilson joined the CICS faculty in 2023. His research explores discrete and computational mathematics, computational social science, networks, and data science.