Constant terms, jagged partitions, and partitions with difference two at distance two

Andrews–Gordon type series for Capparelli's and Göllnitz–Gordon identities

“…A big collection of partition identities awaiting Andrews-Gordon type q-series identities may be found in [23]. The developed machinery does not seem to readily apply, though.…”

Generalizations of Capparelli's identity

“…We begin with a proof of Theorem 1.3 via a constant term identity. This was alluded to at the end of [15], though no details were provided there. We will show that…”

Multi-sum Rogers-Ramanujan Type Identities

“…Indeed, after setting aq = −β 2 1 and replacing z by −z, we see that this identity is equivalent to (3.31). Lovejoy [23] also provided a partition interpretation to (3.36) and hence the identity (3.28) can also be explained as a partition identity.…”

“…Acknowledgements. We thank Jeremy Lovejoy for some valuable comments, especially for bringing the works [13,23,24] to our attention. We are also grateful to Chuanan Wei for helpful comments on the presentation of Corollaries 3.5 and 3.7.…”