Quadratic forms and four partition functions modulo 3.
Overpartition pairs
An overpartition pair is a combinatorial object associated with the -Gauss identity and the summation. In this paper, we prove identities for certain restricted overpartition pairs using Andrews’ theory of recurrences for well-poised basic hypergeometric series and the theory of Bailey chains.
M₂-rank differences for overpartitions
-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.
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