Skip to main content
Department of Mathematics College of Liberal Arts and Sciences

Publications, Preprints & Work in Progress

Listed below are my works in progress and publications and preprints in reverse chronological order:

Here is a link to all my articles on the arXiv: https://arxiv.org/a/dhar_a_2.html

\(\underline{\text{Publications and Preprints}}\):

  1. Euler’s Pentagonal Number Theorem-type results via minimal excludants of partitions and overpartitions (with R. Gupta, A. Mukhopadhyay and R. Sarma) submitted.
  2. Separable integer partition classes and Slater’s list – I (with A. Goswami and R. Li) submitted. [arXiv]
  3. Inequalities for the number of \(t\)-hooks in two partition classes arising from sum-product identities (with B. Kim, E. Kim and A. J. Yee) submitted. [arXiv]
  4. On Glaisher’s Partition Theorem (with G. E. Andrews) submitted. [arXiv]
  5. Further applications of cubic \(q\)-binomial transformations (with A. Berkovich) Discrete Math. 349 (10) (2026) 115204, 8 pp. [arXiv] [DOI]
  6. Finite analogs of partition bias related to hook length two and a variant of Sylvester’s map (with A. Berkovich), Ramanujan J. 68 (4), 2025 (to appear in the special issue in honor of Krishnaswami Alladi: Founding Editor-in-Chief of the Ramanujan Journal). [arXiv] [journal]
  7. On new minimal excludants of overpartitions related to some \(q\)-series of Ramanujan (with A. Mukhopadhyay and R. Sarma), Bull. Aust. Math. Soc. 112 (1), pp 1-13, 2025. [arXiv] [journal]
  8. New Borwein-type conjectures (with A. Berkovich) Exp. Math. (in press). [arXiv] [DOI]
  9. Extension of Bressoud’s generalization of Borwein’s Conjecture and some exact results (with A. Berkovich), Ramanujan J. 67 (16), 2025 (to appear in the special issue in honor of the 85th birthdays of George E. Andrews and Bruce C. Berndt). [arXiv] [journal]
  10. Pfaff’s Method Revisited, to appear in Contributions to Discrete Mathematics. [arXiv]
  11. On partitions with bounded largest part and fixed integral GBG-rank modulo primes (with A. Berkovich) Ann. Comb. 29 (4), 1063-1076, 2025. [arXiv] [journal]
  12. A bijective proof of an identity of Berkovich and Uncu (with A. Mukhopadhyay) to appear in Séminaire Lotharingien de Combinatoire. [arXiv]
  13. On \(_5\psi_5\) identities of Bailey, Int. J. Number Theory, 20 (2), 507-517, 2024. [arXiv] [journal]
  14. Generalization of the Extended Minimal Excludant of Andrews and Newman (with A. Mukhopadhyay and R. Sarma), J. Integer Sequences, 26, 2023, Article 23.3.7. [arXiv] [journal]
  15. Proofs of Two Formulas of Vladeta Jovovic, The Mathematics Student, 93, Nos. 1-2, January – June (2024), 24-29. [arXiv] [journal]

\(\underline{\text{Work in Progress}}\):

  1. Separable integer partition classes and Slater’s list – II (with A. Goswami and R. Li) in preparation.
  2. Fixed Points in Certain Restricted Integer Partitions (with B. Hopkins and J. Sellers) in preparation.
  3. A note on Lehmer-type partition statistics (with A. Malik) in preparation.