Separable Integer Partition Classes (Speaker: Prof. George E Andrews, The Pennsylvania State University)
Sprache des Titels:
Three of the most classical and well-known identities in the theory of partitions concern: (1) the generating function for p(n) (Euler); (2) the generating function for partitions into distinct parts (Euler), and (3) the generating function for partitions in which parts differ by at least 2 (Rogers-Ramanujan). The lovely, simple argument used to produce the relevant generating functions is mostly never seen again. Actually, there is a very general theorem here which we shall present. We then apply it to prove two familiar theorems: (1) Goellnitz-Gordon, and (2) Schur 1926. We also consider an example where the series representation for the partitions in question is new. We close with an application to "partitions with n copies of n." NOTE by Prof. Paule: From 2009-2018 Prof. Andrews was President of the American Mathematical Society (AMS). He is a pioneer in developing the theory of partitions (incl. applications of computer algebra) and a leading researcher in number theory and special functions.