Combinatorial and Algebraic Enumeration: a survey of the work of Ian P. Goulden and David M. Jackson
Algebraic Combinatorics, Volume 5 (2022) no. 6, pp. 1205-1226.

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.

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DOI: 10.5802/alco.269
Classification: 05A05,  05A10,  05E05,  05A15,  05E10,  05E16,  81Q30
Keywords: combinatorial enumeration, factorizations, Lagrange inversion, Hurwitz numbers, KP hierarchy, maps, symmetric functions, immanants
Foley, Angèle M. 1; Morales, Alejandro H. 2; Rattan, Amarpreet 3; Yeats, Karen 4

1 Department of Physics and Computer Science Wilfrid Laurier University 75 University Avenue West Waterloo ON N2L 3C5 (Canada)
2 Department of Mathematics and Statistics, University of Massachusetts, Amherst 710 N. Pleasant Street Amherst MA 01003 (USA)
3 Department of Mathematics, Simon Fraser University 8888 University Dr Burnaby BC V5A 1S6 (Canada)
4 Department of Combinatorics and Optimization, University of Waterloo 200 University Ave W Waterloo ON N2L 3G1 (Canada)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Foley, Angèle M.; Morales, Alejandro H.; Rattan, Amarpreet; Yeats, Karen. Combinatorial and Algebraic Enumeration: a survey of the work of Ian P. Goulden and David M. Jackson. Algebraic Combinatorics, Volume 5 (2022) no. 6, pp. 1205-1226. doi : 10.5802/alco.269. https://alco.centre-mersenne.org/articles/10.5802/alco.269/

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