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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.CO2024
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…
math.CA2024
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…