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On the work of Basil Gordon. (English) Zbl 1086.05002

Basil Gordon has made important contributions to classical analysis, coding theory, group theory, number theory, tilings, difference sets, and combinatorial theory. This article is a well-deserved tribute to his path-breaking discoveries in combinatorics, written by four distinguished collaborators, two of whom are among Gordon’s 26 Ph.D. students. The following aspects of his work are described in detail, together with historical perspective and connections to related work: Rogers-Ramanujan identities; the method of weighted words; plane partitions; congruences for coefficients of modular forms and partition functions; asymptotic methods for partitions and related \(q\)-series. Brief mention is also made of more recent results regarding mock theta functions. There is also a valuable list of 62 references cited in the article, as well as a complete bibliography of 74 papers bearing Gordon’s name as author or coauthor. In the interest of complete disclosure, Gordon’s first paper, published in 1958, is based on his Ph.D. dissertation written at Caltech in 1956 under the reviewer’s direction.

MSC:

05-03 History of combinatorics
11-03 History of number theory
01A70 Biographies, obituaries, personalia, bibliographies
05A17 Combinatorial aspects of partitions of integers
11P81 Elementary theory of partitions
11Fxx Discontinuous groups and automorphic forms
01A60 History of mathematics in the 20th century

Biographic References:

Gordon, Basil
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