On Some Theorems of Hirschhorn#

Abstract

It is found that four theorems of Hirschhorn [Hirschhorn, M. D. (1979). Some partition theorems of the Rogers–Ramanujan type. J. Comb. Th. A 27:33–37] correspond to standard representations of an affine Lie algebra. Using this correspondence two more theorems of the same type are found. It turns out that a classical result of Euler also appears in this context.