21 citations · 71 across the 32 of their papers we have counts for
36 papers
Sum of parts in overpartitions and partitions without repeated odd parts
Frank Garvan, Rishabh Sarma
In this paper, we obtain several Ramanujan-type congruences modulo 5 and 7 for sum of certain non-overlined parts in overpartitions classified by parity and sum of certain parts in…
Congruences modulo powers of and for the crank and rank parity functions and related mock theta functions
Dandan Chen, Rong Chen, Frank Garvan
It is well known that Ramanujan conjectured congruences modulo powers of , and and for the partition function. These were subsequently proved by Watson (1938) and Atkin…
Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts
Frank G. Garvan, Rishabh Sarma
We give combinatorial interpretations of two residual cranks of overpartitions defined by Bringmann, Lovejoy and Osburn in 2009 analogous to the crank of partitions given by Andrew…
Old Meets New: Connecting Two Infinite Families of Congruences Modulo Powers of 5 for Generalized Frobenius Partition Functions
Frank G. Garvan, James A. Sellers, Nicolas Allen Smoot
In 2012 Paule and Radu proved a difficult family of congruences modulo powers of 5 for Andrews' 2-colored generalized Frobenius partition function. The family is associated with th…
New symmetries for Dyson's rank function
F. G. Garvan, Rishabh Sarma
At the 1987 Ramanujan Centenary meeting Dyson asked for a coherent group-theoretical structure for Ramanujan's mock theta functions analogous to Hecke's theory of modular forms. Ma…
Congruences modulo powers of 5 for the rank parity function
Dandan Chen, Rong Chen, Frank Garvan
It is well known that Ramanujan conjectured congruences modulo powers of 5, 7 and and 11 for the partition function. These were subsequently proved by Watson (1938) and Atkin (1967…