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math.NT2026
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…
math.NT2024
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…
math.NT2024
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 $…