# Research

My past and current research.

My current work is focused on combinatorics with a side interest in number theory. I am also interested in history of mathematics. For my publications, see below (arranged in reverse chronological order of publication).

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Some of the papers here may not be the final version that appeared, if you want a latest version send me an email.

## Theses

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

2. 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).

## Peer Reviewed Papers

1. On Deficient Perfect Numbers with Four Distinct Prime Factors, (with Parama Dutta) Asian-European Journal of Mathematics, accepted, 2019, 13 pp. (pdf)

2. 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)

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

4. 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)

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

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

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

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

9. 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)

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

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

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

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

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

## Books

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

## Non Peer-Reviewed Papers

1. Refined Enumeration of Symmetry Classes of Alternating Sign Matrices, (with Ilse Fischer), preprint, 2019. (pdf)

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

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. (pdf)

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

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)

## Lecture Notes

1. Probability Theory (with Rupam Haloi)

## Projects

1. Polya’s Theory of Counting (under Prof. Fernando R. Villegas at The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy), October – December 2014.

2. Some results in Additive Combinatorics and Analytic Number Theory (under Prof. R. Balasubramanian at The Institute of Mathematical Sciences, Chennai, India), June – July 2012.

3. A study of Kummer’s proof of Fermat’s Last Theorem for regular primes (under Prof. Kapil Hari Paranjape at The Indian Institute of Science Education and Research, Mohali, India), June – July 2011.

4. The irrationality of $\zeta(2)$ and $\zeta(3)$ (under Dr. Purusottam Rath at Chennai Mathematical Institute, Chennai, India), June – July 2010.