6 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…
Overpartitions with repeated smallest non-overlined part
Amita Malik, Rishabh Sarma
Inspired by Andrews' and Bachraoui's work on partitions with repeated smallest part, we extend the concept to overpartitions. We study overpartitions with the restriction that the…
Bailey pairs, radial limits of -hypergeometric false theta functions, and a conjecture of Hikami
Jeremy Lovejoy, Rishabh Sarma
In the first part of this paper we prove a conjecture of Hikami on the values of the radial limits of a family of -hypergeometric false theta functions. Hikami conjectured that…
On new minimal excludants of overpartitions related to some -series of Ramanujan
Aritram Dhar, Avi Mukhopadhyay, Rishabh Sarma
Inspired by Andrews' and Newman's work on the minimal excludant or "mex" of partitions, we define four new classes of minimal excludants for overpartitions and establish relations…
Transformation and symmetries for the Andrews-Garvan crank function
Rishabh Sarma
Let be the two-variable generating function of Dyson's rank function. In a recent joint work with Frank Garvan, we investigated the transformation of the elements of the $…
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…