A Rademacher type formula for partitions and overpartitions.
Combinatorial interpretations for identities using chromatic partitions
We provide combinatorial interpretations for three new classes of partitions, the so-called chromatic partitions. Using only combinatorial arguments, we show that these partition identities resemble well-know ordinary partition identities.
Hybrid proofs of the -binomial theorem and other identities.
-rank differences for partitions without repeated odd parts
We prove formulas for the generating functions for -rank differences for partitions without repeated odd parts. These formulas are in terms of modular forms and generalized Lambert series.
New identities for the Rogers-Ramanujan functions
On Bailey pairs and certain q-series related to quadratic and ternary quadratic forms
We provide a new approach to establishing certain q-series identities that were proved by Andrews, and show how to prove further identities using conjugate Bailey pairs. Some relations between some q-series and ternary quadratic forms are established.
On Some Partition Functions Related to Some Mock Theta Functions
We show that some partitions related to two of Ramanujan's mock theta functions are related to indefinite quadratic forms and real quadratic fields. In particular, we examine a third order mock theta function and a fifth order mock theta function.
Parity indices of partitions
Rogers-Ramanujan-Slater type identities.
Self-conjugate vector partitions and the parity of the spt-function
Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coefficients of a certain mock theta function studied by the first author,...
Series and iterations for 1/π