I am primarily interested in Combinatorics and Graph Theory. Recently I am also becoming interested in Finite Group Theory. Below I note down some projects I am planning for my future research.
Gamma positivity and log-concavity of various combinatorial sequences.
q-analogues of problems in extremal set theory.
Signed enumeration of various statistics over Coxeter groups.
Extremal problems related to vertex connectivity, domination number and other interesting parameters of graphs associated to groups.
Combinatorial properties of finite groups.
Combinatorial properties of the character table of a finite group.
21. A descent-excedance correspondence in colored permutation groups, with Umesh Shankar and Sivaramakrishnan Sivasubramanian, accepted in Enumerative Combinatorics and Applications, 2025.
20. Sign-balance of excedances over mod-k-alternating permutations and gamma-positivity, with Iswar Mahato, accepted in Journal of Algebraic Combinatorics, 2025.
19. On the domination number of proper power graphs of finite groups, with Sudip Bera, Kamal Lochan Patra, Binod Kumar Sahoo, Discrete Mathematics, Vol 348, Issue 10, 2025.
18. On the order sequence of a group, with Peter J. Cameron, Electronic Journal of Combinatorics, Vol 32, Issue 2, 2025.
17. Enumerating alternating-runs with sign in Type A and Type B Coxeter groups, with Sivaramakrishnan Sivasubramanian, Discrete Mathematics, Vol 348, Issue 6, 2025.
16. An exact enumeration of vertex connectivity of the enhanced power graphs of finite nilpotent groups, with Sudip Bera, Vol 175, Page 550-561, Acta Mathematica Hungarica, 2025.
15. On the sum of the entries in a character table, with Arvind Ayyer, and Digjoy Paul, Séminaire Lotharingien de Combinatoire, 91B Article #99, 12 pp, Proceedings of the 36th Conference on Formal Power Series and Algebraic Combinatorics (Bochum), 2024.
14. On the difference of the enhanced power graph and the power graph of a finite group, with Sucharita Biswas, Peter J. Cameron, and Angsuman Das, Journal of Combinatorial Theory, Series A, Vol 208, November 2024, 105932, 2024.
13. An exact upper bound for the sum of powers of element orders in non-cyclic finite groups, with Archita Mondal, Journal of Pure and Applied Algebra, Vol 228, Issue 6, 107580, 2024.
12. On the alternating runs polynomial in type B and type D Coxeter groups, with Sivaramakrishnan Sivasubramanian, Journal of the Ramanujan Mathematical Society, Vol 38, Issue 3, page 215-223, 2023.
11. q-Enumeration of Type B and Type D Eulerian Polynomials Based on Parity of Descents, with Umesh Shankar and Sivaramakrishnan Sivasubramanian, accepted in Enumerative Combinatorics and Applications, Vol 4, Article #S2R3, 2024.
10. Signed alternating descent enumeration in Classical Weyl Groups, with Sivaramakrishnan Sivasubramanian, Discrete Mathematics, Vol 346, Issue 10, 2023, 113540. 2023.
9. Interlacing of zeroes of certain real-rooted polynomials, Archiv Der Mathematik, Vol 120, pp 456-466, 2023.
8. On Some Properties of Vector Space based graphs, with Peter Cameron, and Angsuman Das, Vol 71, Issue 17, Linear and Multilinear Algebra, 2022.
7. On the proper enhanced power graphs of finite nilpotent groups, with Sudip Bera, Journal of Group Theory, Vol 25(6), 2022.
6. Determining Number of Kneser Graphs: Exact Values and Improved Bounds, with Angsuman Das, Discrete Mathematics & Theoretical Computer Science, Vol 24(1), 2022.
5. Eulerian Central Limit Theorems and Carlitz identities in positive elements of Classical Weyl Groups, with Sivaramakrishnan Sivasubramanian, Journal of Combinatorics, Vol 13(3), pp 333-356, 2022.
4. Log-concavity of the Excedance Enumerators in positive elements of Type A and Type B Coxeter Groups, Discrete Mathematics, Vol 344(7), pp 112392, 2021.
3. On the connectivity of enhanced power graphs of finite groups, with Sudip Bera and Sajal Kumar Mukherjee, Graphs and Combinatorics, Vol 37(2), pp 591-603, 2021.
2. Gamma Positivity of the Excedance-Based Eulerian Polynomial in Positive Elements of Classical Weyl Groups, with Sivaramakrishnan Sivasubramanian, Annals of Combinatorics, Vol 24, pp 711-738, 2020.
1. Gamma positivity of the Descent based Eulerian polynomial in positive elements of Classical Weyl Groups, with Sivaramakrishnan Sivasubramanian, Electronic Journal of Combinatorics, P3.20, 27(3), 2020.
1. The solvability of a finite group by the sum of powers of element orders, submitted, https://arxiv.org/abs/2212.07748.
2. Sharp lower bound on the "number of nodal decomposition" of graphs, with Soumyajit Saha, submitted, https://arxiv.org/abs/2303.08417.
3. How large is the character degree sum compared to the character table sum for a finite group? with Arvind Ayyer and Digjoy Paul, https://arxiv.org/abs/2406.06036.
4. q-analogues of Fisher's inequality and oddtown theorem, https://arxiv.org/pdf/2505.15664.