Research

My past and current research.

My current work is focused on combinatorics (enumerative and algebraic), $q$-series and integer partitions, with a strong interest in some aspects of theoretical computer science. For some of my work, see below (arranged in reverse chronological order of publication, some of the papers here may not be the final version that appeared).

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Preprints

  1. Combinatorial Proofs of Some Results of Andrews and El Bachraoui, (with Pankaj Jyoti Mahanta), preprint, 2024. (pdf)

  2. Symmetric Domino Tilings of Aztec Diamonds, (with Pravakar Paul), preprint, 2024. (pdf)

  3. A Novel Approach to Counting Perfect Matchings of Graphs, (with Pravakar Paul), preprint, 2024. (pdf)

  4. Congruences for Andrews-Uncu’s partition function $\mathcal{EO}_u(n)$, (with Nayandeep Deka Baruah, Hirakjyoti Das and Abhishek Sarma), preprint, 2024.

  5. The Signed Roman Domination Number of Ladder graphs, circular Ladder graphs and their complements, (with Dilbak Haje, Delbrin Ahmed, and Hassan Izanloo), preprint, 2024. (pdf)

  6. Arithmetic Properties Modulo Powers of $2$ and $3$ for Overpartition $k$-Tuples with Odd Parts, (with Hirakjyoti Das and Abhishek Sarma), preprint, 2024. (pdf)

  7. On near $F_k$-perfect and deficient $F_k$-perfect numbers, (with Flora S. Jeba, Pankaj Jyoti Mahanta and Anirban Roy), preprint, 2024.

  8. Biases in Non-Unitary Partitions, (with Pankaj Jyoti Mahanta and Abhishek Sarma), preprint, 2022. (pdf)

Peer Reviewed Papers

  1. Further Arithmetic Properties of Overcubic Partition Triples, (with Abhishek Sarma), Bulletin of the Australian Mathematical Society, accepted, 2024. (pdf)

  2. Arithmetic Properties Modulo Powers of $2$ for Overpartition $k$-Tuples with Odd Parts, (with Abhishek Sarma and James A. Sellers), Journal of the Ramanujan Mathematical Society, accepted, 2024. (pdf)

  3. On $k$-Facile Perfect Numbers, (with Flora S. Jeba and Anirban Roy), Springer Proceedings of International Conference on Algebra and its Applications 2023, Fez, Morocco, to appear, 2024. (pdf)

  4. Ramanujan-type Congruences for Partition $k$-Tuples with $5$-Cores, (with Abhishek Sarma and Pranjal Talukdar), Indian Journal of Pure and Applied Mathematics, accepted, 2024. (pdf)

  5. Extensions of some results of Jovovic and Dhar, (with Pankaj Jyoti Mahanta), Journal of the Ramanujan Mathematical Society, accepted, 2024. (pdf)

  6. On near-perfect numbers with five prime factors, (with Flora Jeba S and Anirban Roy), Advances in Mathematical and Computational Sciences: Proceedings of The ICRTMPCS International Conference 2023, De Gruyter Proceedings in Mathematics, De Gruyter, 207-220, 2025. (pdf)

  7. Further congruences for $(4,8)$-regular bipartition quadruples modulo powers of $2$, Journal of the Assam Academy of Mathematics, 2024, 14, 1-5. (pdf)

  8. Conjectures on congruences of binomial coefficients modulo higher powers of a prime number, Journal of the Assam Academy of Mathematics, Journal of the Assam Academy of Mathematics, 2023, 13, 5-7. (pdf)

  9. Some Missed Congruences modulo powers of $2$ for $t$-colored overpartitions, Boletín de la Sociedad Matemática Mexicana, 2023, 29 (1), Article 15, 10 pp. (pdf)

  10. Representing Even Perfect and Near-Perfect Numbers as Sums of Cubes, (with Padma Bhushan Borah and Pankaj Jyoti Mahanta), Journal of the Assam Academy of Mathematics, 2022, 12, 1-7. (pdf)

  11. Parity Biases in Partitions and Restricted Partitions, (with Koustav Banerjee, Sreerupa Bhattacharjee, Manosij Ghosh Dastidar and Pankaj Jyoti Mahanta), Séminaire Lotharingien de Combinatoire (Proceedings of the 34th Conference on Formal Power Series and Algebraic Combinatorics 2022 (Bangalore)), 86B.21, 2022. (pdf)

  12. Refinement of some partition identities of Merca and Yee, (with Pankaj Jyoti Mahanta), International Journal of Number Theory, 2022, 18 (5), 1131-1142. (pdf)

  13. Some New and Old Gibonacci Identities, (with Pankaj Jyoti Mahanta), Rocky Mountain Journal of Mathematics, 2022, 52 (2), 645-665. (pdf)

  14. Parity Biases in Partitions and Restricted Partitions, (with Koustav Banerjee, Sreerupa Bhattacharjee, Manosij Ghosh Dastidar and Pankaj Jyoti Mahanta), European Journal of Combinatorics, 2022, 103, 103522, 19 pp. (pdf)

  15. Refined Enumeration of Symmetry Classes of Alternating Sign Matrices, (with Ilse Fischer), Journal of Combinatorial Theory, Series A, 2021, 178, 105350, 51 pp. (pdf)

  16. A family of lacunary recurrences for Lucas Numbers, (with Pankaj Jyoti Mahanta), The Fibonacci Quarterly, 2020, 58 (4), 356-360. (pdf)

  17. Some properties of Zumkeller numbers and $k$-layered numbers, (with Pankaj Jyoti Mahanta and Daniel Yaqubi), Journal of Number Theory, 2020, 217, 218–236. (pdf)

  18. Hard and Easy Instances of L-Tromino Tilings, (with Javier T. Akagi, Carlos F. Gaona, Fabricio Mendoza and Marcos Villagra) Theoretical Computer Science, 2020, 815, 197-212. (pdf)

  19. On Deficient Perfect Numbers with Four Distinct Prime Factors, (with Parama Dutta) Asian-European Journal of Mathematics, 2020, 13 (7), 2050126, 13 pp. (pdf)

  20. Hard and Easy Instances of L-Tromino Tilings, (with Javier T. Akagi, Carlos F. Gaona, Fabricio Mendoza and Marcos Villagra) Proceedings of the 13th International Conference and Workshops on Algorithms and Computation (WALCOM) 2019, Lecture Notes in Computer Science (LNCS), Volume 11355, Springer, 2019, 82-95. (pdf)

  21. Enumeration of Domino Tilings of an Aztec Rectangle with boundary defects, Advances in Applied Mathematics, 2017, 89, 41–66. (pdf)

  22. Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial Sequences, (with Alexandre Laugier) Kyungpook Mathematical Journal, 2017, 57 (1), 1–84. (pdf)

  23. Some Results on Generalized Multiplicative Perfect Numbers, (with Alexandre Laugier and Upam Sarmah) Annali Dell’Universita’ di Ferrara, 2016, 62 (2), 293–312. (pdf)

  24. A combinatorial proof of a result on generalized Lucas Polynomials, (with Alexandre Laugier) Demonstratio Mathematica, 2016, 49 (3), 266–270.

  25. A study of the crank function in Ramanujan’s Lost Notebook, The Mathematics Student, 2015, 84 (1-2), 105 — 121. (pdf)

  26. Some results about Linear Recurrence Relation Homomorphisms, (with Alexandre Laugier) Notes on Number Theory and Discrete Mathematics, 2014, 20 (4), 58 — 68. (pdf)

  27. A characterization of a prime $p$ from the binomial coefficient ${n \choose p}$, (with Alexandre Laugier), The Mathematics Student, 2014, 83 (1-4), 221 — 227. (pdf)

  28. Cranks in Ramanujan’s Lost Notebook, Journal of the Assam Academy of Mathematics, 2013, 6, 59 — 63. (pdf)

  29. A new proof of Lucas’ Theorem, (with Alexandre Laugier) Notes on Number Theory and Discrete Mathematics, 2012, 18 (4), 1 — 6. (pdf)

  30. Binomial Symbols and Prime Moduli, (with Jure Vogrinc) Journal of the Indian Mathematical Society, 2011, 79 (1-4), 137 — 143. (pdf)

  31. A Simple Number Theoretic Result, (with Jure Vogrinc) Journal of the Assam Academy of Mathematics, 2010, 3, 91 — 96. (pdf)

Books

  1. Moha Moha Puruxor Sanekire Jibonor (edited with Pankaj Jyoti Mahanta), Panchajanya Publishers, Guwahati, 2018.

  2. The Pursuit of Joy (with Pankaj Jyoti Mahanta), LAP Lambert Academic Publishing, Germany, 2011.

Theses

  1. Topics on Alternating Sign Matrices and Aztec Rectangles, Doctoral Thesis, University of Vienna (Vienna, Austria), 2019. (Supervisor: Prof. Ilse Fischer) (pdf).

  2. Representations of the Symmetric Group, Diploma Thesis, The Abdus Salam International Centre for Theoretical Physics (Trieste, Italy), 2015. (Supervisor: Prof. Fernando R. Villegas)

  3. A study of the crank function with special emphasis on Ramanujan’s Lost Notebook, M.Sc Thesis, Tezpur University (Tezpur, India), 2014. (Supervisor: Prof. Nayandeep Deka Baruah) (pdf).

Solutions to Problems

  1. Solution to Problem 4 of The Mathematics Student, 2015 (1-2), The Mathematics Student, July — December 2015, 84 (3-4), 181.

  2. Solution to Problem 1908 of Mathematics Magazine, (with Bishal Deb), The Mathematics Magazine, December 2013, 86 (5), 384 — 385.

Non Peer-Reviewed Papers

  1. Almost Circular Balancing Numbers, Advances in Mathematical Sciences (Z. Ahmed (ed.)), Empyreal Publishing House, 2019, 61 — 67. (pdf)

  2. On Deficient Perfect Numbers with Four Distinct Prime Factors, II, preprint, 2018. (pdf)

  3. The Perils of the Indian Education System, (with Madhurrya P. Talukdar) Pragyan, Tinisukia College Magazine, 2019. (pdf)

  4. John Forbes Nash, Jr. – A Short Obituary, Asia Pacific Mathematics Newsletter, September 2015, 5 (2), 42 — 43.

  5. The Pythagoras’ Theorem, Asia Pacific Mathematics Newsletter, September 2015, 5 (2), 5 — 8.

  6. Periodic Sequences modulo $m$, (with Alexandre Laugier) prepint, 2015. (pdf)

  7. Gonit Sora-the two year journey, (with Pankaj Jyoti Mahanta), Asia Pacific Mathematics Newsletter, October 2013, 3 (4), 25 — 27. (pdf)

  8. An interesting number theoretic problem, Ganit Bikash, 2011. (pdf)