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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.

On Some Partition Functions Related to Some Mock Theta Functions

Alexander E. Patkowski (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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.

Self-conjugate vector partitions and the parity of the spt-function

George E. Andrews, Frank G. Garvan, Jie Liang (2013)

Acta Arithmetica

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,...

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