My research interests lie in number theory and combinatorics related to integer partitions, mock theta functions, and q-series.
Publications
2-elongated plane partitions and powers of 7: the localization method applied to a genus 1 congruence family, Canadian Journal of Mathematics (accepted for publication), (Supplementary file) (with N. A. Smoot).
The localization method applied to k-elongated plane partitions and divisibility by 5, Mathematische Zeitschrift (2025), (with N. A. Smoot).
Invariants of quartic binary form and proofs of Chen’s conjectures on inequalities for the partition function and the Andrews’ spt function, Research in the Mathematical Sciences (2025).
The Jensen-Pólya program. Internationale Mathematische Nachrichten, Austrian Math. Soc. (2024).
A unified framework to prove multiplicative inequalities for the partition function. Advances in Applied Mathematics (2024).
Positivity of second shifted difference of partitions and overpartitions: a combinatorial approach, Enumerative Combinatorics and Applications (2023).
Error bounds for the asymptotic expansion of the partition function, Rocky Mountain Journal of Mathematics (with P. Paule, C. S. Radu, and C. Schneider).
Inequalities for the modified Bessel function of first kind of non-negative order, Journal of Mathematical Analysis and Applications (2023) .
Hook type tableaux and partition identities, Notes on Number Theory and Discrete Mathematics (2022) (with M. G. Dastidar).
Ramanujan's theta functions and parity of parts and cranks of partitions. Annals of Combinatorics (2022) (with M. G. Dastidar).
New inequalities for p(n) and log p(n). Ramanujan Journal (2022). (with P. Paule, C. S. Radu, and W. H. Zeng).
Parity biases in partitions and restricted partitions. European Journal of Combinatorics (2022), (with S. Bhattacharjee, M. G. Dastidar, P. J. Mahanta, and M. P. Saikia).
Parity biases in partitions and restricted partitions (extended abstract). Séminaire Lotharingien de Combinatoire, 86B, article #21 (Proceedings of the 34th Conference on Formal Power Series and Algebraic Combinatorics 2022 (Bangalore)), (2022) [url]. (with S. Bhattacharjee, M. G. Dastidar, P. J. Mahanta, and M. P. Saikia).
An elementary alternative proof for Chan’s analogue of Ramanujan’s most beautiful identity and some inequality of the cubic partition. Notes on Number Theory and Discrete Mathematics (2017). (with P. D. Adhikary).
New representations for sigma(q) via reciprocity theorems,. In: Analytic Number Theory, Modular Forms and q- Hypergeometric Series, George Andrews, Frank Garvan (ed.) (2016) [url]. (with A. Dixit).
Preprints
A generic approach to proving Turán-type inequalities for sequences that admit exact formulas, with an application to unimodal sequences (with K. Bringmann and B. Kane), submitted for publication.
Asymptotics for the reciprocal and shifted quotient of the partition function (with P. Paule, C. S. Radu, and C. Schneider), submitted for publication.