Sequences in overpartitions.

This paper is devoted to the study of sequences in overpartitions and their relation to 2-color partitions. An extensive study of a general class of double series is required to achieve these ends.

Weighted cylindric partitions.

Recently Corteel and Welsh outlined a technique for finding new sum-product identities by using functional relations between generating functions for cylindric partitions and a theorem of Borodin. Here, we extend this framework to include very general product-sides coming from work of Han and Xiong. In doing so, we are led to consider structures such as weighted cylindric partitions, symmetric cylindric partitions and weighted skew double-shifted plane partitions. We prove some new identities and obtain new proofs of known identities, including the Göllnitz-Gordon and Little Göllnitz identities as well as some beautiful Schmidt-type identities of Andrews and Paule.