Let S denote a subset of the positive integers, and let pS(n) be the associated partition function, that is pS(n) denotes the number of partitions of the positive integer n into parts taken from S.… (More)

Theorems in the theory of partitions are closely related to basic hypergeometric series. Some identities arising in basic hypergeometric series can be interpreted in the theory of partitions using… (More)

A lecture hall partition of length n is a sequence (λ1, λ2, . . . , λn) of nonnegative integers satisfying 0 ≤ λ1/1 ≤ · · · ≤ λn/n. M. Bousquet-Mélou and K. Eriksson showed that there is an one to… (More)

In his lost notebook, Ramanujan recorded a formula relating a “character analogue” of the Dedekind eta-function, the integral of a quotient of eta-functions, and the value of a Dirichlet Lfunction at… (More)

Ramanujan’s lost notebook contains several identities arising from the Rogers–Fine identity and/or Rogers’ false theta functions. Combinatorial proofs for many of these identities are given.

The research described in this paper was motivated by an enigmatic entry in Ramanujan’s lost notebook [11, p. 45] in which he claimed, in an unorthodox fashion, that a certain q-continued fraction… (More)

Euler’s partition theorem states that the number of partitions of an integer N into odd parts is equal to the number of partitions of N in which the ratio of successive parts is greater than 1. It… (More)

G. E. Andrews has established a refinement of the generating function for partitions π according to the numbers O(π) and O(π′) of odd parts in π and the conjugate of π, respectively. In this paper,… (More)