Rank partition functions and truncated theta identities

Partition Identities Arising from Theta Function Identities

The authors show that certain theta function identities of Schröter and Ramanujan imply elegant partition identities.

Asymptotics for Rank Partition Functions

In this paper, we obtain asymptotic formulas for an infinite class of rank generating functions. As an application, we solve a conjecture of Andrews and Lewis on inequalities between certain ranks.

Factorization of rank two theta functions

Partition Identities

A partition of a positive integer n (or a partition of weight n) is a non-decreasing sequence λ = (λ1, λ2, . . . , λk) of non-negative integers λi such that ∑k i=1 λi = n. The λi’s are the parts of the partition λ. Integer partitions are of particular interest in combinatorics, partly because many profound questions concerning integer partitions, solved and unsolved, are easily stated, but not ...

Cyclic Identities Involving Ratios of Jacobi Theta Functions

Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at p equally shifted points were recently found. The purpose of this paper is to re-express these cyclic identities in terms of ratios of Jacobi theta functions, since many physicists prefer using Jacobi theta functions rather than Jacobi elliptic functions.