# 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.

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

## Peer Reviewed Papers

1. A Simple Number Theoretic Result, (with Jure VogrincJournal of the Assam Academy of Mathematics, 2010, 3, 91 — 96. (pdf)
2. Binomial Symbols and Prime Moduli, (with Jure VogrincJournal of the Indian Mathematical Society, 2011, 79 (1-4), 137 — 143. (pdf)
3. A new proof of Lucas’ Theorem, (with Alexandre LaugierNotes on Number Theory and Discrete Mathematics, 2012, 18 (4), 1 — 6. (pdf)
4. Cranks in Ramanujan’s Lost NotebookJournal of the Assam Academy of Mathematics, 2013, 6, 59 — 63. (pdf)
5. 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)
6. Some results about Linear Recurrence Relation Homomorphisms, (with Alexandre LaugierNotes on Number Theory and Discrete Mathematics, 2014, 20 (4), 58 — 68. (pdf)
7. A study of the crank function in Ramanujan’s Lost NotebookThe Mathematics Student, 2015, 84 (1-2), 105 — 121. (pdf)
8. A combinatorial proof of a result on generalized Lucas Polynomials, (with Alexandre LaugierDemonstratio Mathematica, 2016, 49 (3), 266–270. (pdf)
9. Some Results on Generalized Multiplicative Perfect Numbers, (with Alexandre Laugier, Upam SarmahAnnali Dell’Universita’ di Ferrara, 2016, 62 (2), 293–312. (pdf)
10. Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial Sequences, (with Alexandre LaugierKyungpook Mathematical Journal, 2017, 57 (1), 1–84. (pdf)
11. Enumeration of Domino Tilings of an Aztec Rectangle with boundary defectsAdvances in Applied Mathematics, 2017, 89, 41–66. (pdf)

## Solutions to Problems

1. Solution to Problem 1908 of Mathematics Magazine, (with Bishal Deb), The Mathematics Magazine, December 2013, 86 (5), 384 — 385. (pdf)
2. Solution to Problem 4 of The Mathematics Student, 2015 (1-2)The Mathematics Student, July — December 2015, 84 (3-4), 181. (pdf)

## Books

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

## Non Peer-Reviewed Papers

1. An interesting number theoretic problemGanit Bikash, 2011. (pdf)
2. Gonit Sora-the two year journey, (with Pankaj Jyoti Mahanta), Asia Pacific Mathematics Newsletter, October 2013, 3 (4), 25 — 27. (pdf)
3. Periodic Sequences modulo $m$, (with Alexandre Laugierprepint, 2015. (pdf)
4. The Pythagoras’ TheoremAsia Pacific Mathematics Newsletter, September 2015, 5 (2), 5 — 8. (pdf)
5. John Forbes Nash, Jr. – A Short ObituaryAsia Pacific Mathematics Newsletter, September 2015, 5 (2), 42 — 43. (pdf)

## Lecture Notes

1. Probability Theory (with Rupam Haloi)

## Projects

1. The irrationality of $\zeta(2)$ and \$\zeta(3) (under Dr. Purusottam Rath at Chennai Mathematical Institute, Chennai, India), June – July 2010.
2. 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.
3. Some results in Additive Combinatorics and Analytic Number Theory (under Prof. R. Balasubramanian at The Institute of Mathematical Sciences, Chennai, India), June – July 2012.
4. Polya’s Theory of Counting (under Prof. Fernando R. Villegas at The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy), October – December 2014.