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M 2 -rank differences for partitions without repeated odd parts

Jeremy Lovejoy, Robert Osburn (2009)

Journal de Théorie des Nombres de Bordeaux

We prove formulas for the generating functions for M 2 -rank differences for partitions without repeated odd parts. These formulas are in terms of modular forms and generalized Lambert series.

Mock modular forms and singular combinatorial series

Amanda Folsom, Susie Kimport (2013)

Acta Arithmetica

A celebrated result of Bringmann and Ono shows that the combinatorial rank generating function exhibits automorphic properties after being completed by the addition of a non-holomorphic integral. Since then, automorphic properties of various related combinatorial families have been studied. Here, extending work of Andrews and Bringmann, we study general infinite families of combinatorial q-series pertaining to k-marked Durfee symbols, in which we allow additional singularities. We show that these...

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