Addition and counting: The arithmetic of partitions (Q2756782)

The aim of this article is ``to describe to a general mathematical audience some of the important advances in partition theory over the past century and to highlight some of its connections to other areas of mathematics''.NEWLINENEWLINENEWLINEThe article begins with a discussion of classical results, such as Euler's generating function and recurrence, the Hardy-Ramanujan-Rademacher formula, Ramanujan's congruences, Dyson's rank and crank and some examples of Atkin. The last third of the article outlines some recent developments involving modular forms and \(L\)-functions.NEWLINENEWLINENEWLINEFor a letter to the editor about this article, and Ahlgren and Ono's reply to this letter, please see [\textit{M. Hirschhorn}, Ramanujan's partition congruences, Discrete Math. 131, 351-355 (1994; Zbl 0802.05004), and \textit{S. Ahlgren} and \textit{K. Ono}, ``Response to Hirschhorn'', Letters to the Editor, Notices Am. Math. Soc. 49, 758 (2002).