# Dr Manjil Saikia

Research Associate

- saikiam@cardiff.ac.uk
- 5.36, Abacws, Senghennydd Road, Cathays, Cardiff, CF24 4AG

## Overview

### Current Research

- Enumerative Combinatorics (alternating sign matrices, lattice paths, plane partitions, lozenge tilings, domino tilings, etc.)
- Elementary Number Theory (Diophantine equations, perfect numbers, etc.)
- Partitions and q-series

## Biography

### Education

- Dr. rer. nat. (Doctor of Natural Sciences) in Mathematics, University of Vienna, Austria, 2019.
- Postgraduate Diploma in Mathematics, The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy, 2015.
- M.Sc. in Mathematics, Tezpur University, India, 2014.

### Other Activities

- Managing Editor, Gonit Sora (a bilingual website devoted to mathematics)

### Professional memberships

- American Mathematical Society
- Ramanujan Mathematical Society
- Assam Academy of Mathematics

### Speaking engagements

- Combinatory Analysis 2018: A Conference in Honor of George Andrews’ 80th birthday, Pennsylvania State University, State College, USA, July 2018 (contributed talk)
- Vienna Discrete Mathematics Seminar, Technische Universität Wien, April 2018
- 80th Séminaire Lotharingien de Combinatoire, Institut Camille Jordan - Bâtiment Braconnier, Université Claude Bernard Lyon 1, France, March 2018 (contributed talk)
- PhD Colloquium, Fakultät für Mathematik, Universität Wien, Austria, March 2018 (invited talk)
- First Interdisciplinary Symposium of the Vienna Doctoral Schools, Universität Wien, Austria,September 2017 (contributed talk)
- Mini-Conference on Networks and Games, Indian Statistical Institute, Kolkata, India, July 2017 (invited talk)
- Stat-Math Unit Seminar, Indian Statistical Institute, Delhi, India, February 2017
- International Conference of The Indian Mathematics Consortium in cooperation with American Mathematical Society, Banaras Hindu University, Varanasi, India, December 2016 (contributed talk)
- ALEA in Europe Young Researcher’s Workshop, Technische Universität Wien, Austria, September 2016 (contributed talk)
- 13rd Algorithmic and Ennumerative Combinatorics Summer School, Research Institute for Symbolic Computation, Johannes Kepler Universität Linz, August 2016 (contributed talk)
- Vienna Discrete Mathematics Seminar, Technische Universität Wien, June 2016
- National Seminar on Advances in Mathematical Sciences, Gauhati University, December 2015 (contributed talk)
- ICM International Satellite Conference on Rings and Near Rings, North Eastern Hill University, Shillong, India, September 2010 (invited talk)

### Committees and reviewing

- Journal reviewer: Advances in Mathematics, Journal of Algebraic Combinatorics, Annals of Combinatorics, Discrete Mathematics, Mathematica Slovaca, Journal of the Indian Mathematical Society, Mathematics Student, etc.
- Reviewer, Mathematical Reviews of the American Mathematical Society
- Reviewer, Zentralblatt Math

## Publications

### 2022

- Mahanta, P. J. and Saikia, M. 2022. Some new and old Gibonacci identities. Rocky Mountain Journal of Mathematics 52(2), pp. 645-665. (10.1216/rmj.2022.52.645)
- Banerjee, K., Bhattacharjee, S., Dastidar, M. G., Mahanta, P. J. and Saikia, M. P. 2022. Parity biases in partitions and restricted partitions. European Journal of Combinatorics 103, article number: 103522. (10.1016/j.ejc.2022.103522)

### 2021

- Mahanta, P. J. and Saikia, M. P. 2021. Refinement of some partition identities of Merca and Yee. International Journal of Number Theory 18(5), pp. 1131-1142.
- Fischer, I. and Saikia, M. 2021. Refined enumeration of symmetry classes of alternating sign matrices. Journal of Combinatorial Theory, Series A 178, article number: 105350. (10.1016/j.jcta.2020.105350)

### 2020

- Mahanta, P., Saikia, M. and Yaqubi, D. 2020. Some properties of Zumkeller numbers and k-layered numbers. Journal of Number Theory 217(12), pp. 218-236. (10.1016/j.jnt.2020.05.003)
- Dutta, P. and Saikia, M. 2020. On deficient perfect numbers with four distinct prime factors. Asian-European Journal of Mathematics 13(7), article number: 2050126. (10.1142/S1793557120501260)
- Mahanta, P. J. and Saikia, M. P. 2020. A family of lacunary recurrences for Lucas Numbers. The Fibonacci Quarterly 38(4), pp. 356-360.
- Akagi, J. T., Gaona, C. F., Mendoza, F., Saikia, M. and Villagra, M. 2020. Hard and easy instances of L-tromino tilings. Theoretical Computer Science 815, pp. 197-212. (10.1016/j.tcs.2020.02.025)

### 2018

- Akagi, J. T., Gaona, C. F., Mendoza, F., Saikia, M. and Villagra, M. 2018. Hard and easy instances of L-Tromino tilings. Presented at: International Workshop on Algorithms and Computation, Guwahati, India, 27 Feb - 2 Mar 2019WALCOM: Algorithms and Computation, Vol. 11355. Springer Verlag pp. 82-95., (10.1007/978-3-030-10564-8_7)

### 2017

- Saikia, M. 2017. Enumeration of domino tilings of an Aztec rectangle with boundary defects. Advances in Applied Mathematics 89, pp. 41-66. (10.1016/j.aam.2017.04.002)
- Laugier, A. and Saikia, M. P. 2017. Some properties of Fibonacci dumbers, deneralized Fibonacci numbers and generalized Fibonacci polynomial sequences. Kyungpook mathematical journal 57(1), pp. 1-84. (10.5666/KMJ.2017.57.1.1)

### 2016

- Laugier, A., Saikia, M. P. and Sarmah, U. 2016. Some results on generalized multiplicative perfect numbers. Annali dell'Universita di Ferrara 62(2), pp. 293-312. (10.1007/s11565-016-0248-9)
- Laugier, A. and Saikia, M. P. 2016. A combinatorial proof of a result on generalized Lucas polynomials. Demonstratio Mathematica 49(3), pp. 266-270. (10.1515/dema-2016-0022)

### 2015

- Saikia, M. 2015. A study of the crank function in Ramanujan's Lost Notebook. The Mathematics Student 84(1-2), pp. 105-121.

### 2014

- Saikia, M. and Laugier, A. 2014. A characterization of a prime p from the binomial coefficient (np). The Mathematics Student 83(1-4), pp. 221-227.
- Laugier, A. and Saikia, M. 2014. Some results about linear recurrence relation homomorphisms. Notes on Number Theory and Discrete Mathematics 20(4), pp. 58-68.

### 2012

- Laugier, A. and Saikia, M. 2012. A new proof of Lucas' Theorem. Notes on Number Theory and Discrete Mathematics 18(4), pp. 1-6.

### 2011

- Saikia, M. and Mahanta, P. 2011. The pursuit of joy: Volume 1. Lambert Academic Publishing.
- Saikia, M. and Vogrinc, J. 2011. Binomial symbols and prime moduli. The Journal of the Indian Mathematical Society 78(1-4), pp. 136-143.

I am broadly interested in enumerative and algebraic combinatorics with a strong side interest in number theory and analysis of algortihms. Most of my papers are on the arXiv.