Research

Papers

1. Towards decidability of conjugacy of pairs and triples, with Benny George, Logic and its applications, Lecture Notes in Computer Science, 2009. 

2. Block companion singer cycles, primitive recursive vector sequences, and coprime polynomial pairs over finite fields, with Sudhir Ghorpade. Finite Fields and Their Applications, 2011. arXiv

3. Relatively prime polynomials and nonsingular Hankel matrices over finite fields, with Mario García-Armas and Sudhir Ghorpade. Journal of Combinatorial Theory, Series A, 2011. arXiv

4. Enumeration of splitting subspaces over finite fields, with Sudhir Ghorpade, Arithmetic, Geometry, Cryptography and Coding Theory, (Luminy, France, March 2011), Contemporary Mathematics, American Mathematical Society, 2012. arXiv

5. Arithmetic progressions in a unique factorization domain, with Sudhir Ghorpade, Acta Arithmetica, 2012. arXiv

6. Enumeration of linear transformation shift registers, Designs, Codes and Cryptography, 2015. arXiv

7. A new proof of Fitzgerald’s characterization of primitive polynomials, Finite Fields and Their Applications, 2015. arXiv

8. Counting zero kernel pairs over a finite field, Linear Algebra and its Applications, 2016. arXiv

9. The number of linear transformations defined on a subspace with given invariant factors, Linear Algebra and its Applications, 2017. arXiv

10. Hypersurfaces in weighted projective spaces over finite fields with applications to coding theory, with Yves Aubry, Wouter Castryck, Sudhir Ghorpade, Gilles Lachaud, and Michael E. O'Sullivan, Association for Women in Mathematics Series 9, 2017 (Proceedings of Algebraic Geometry for Cryptography and Coding Theory, IPAM, UCLA). arXiv

11. Unimodular polynomial matrices over finite fields, with Akansha Arora and Ayineedi Venkateswarlu, Journal of Algebraic Combinatorics, 2020. arXiv

12. Enumerating partial linear transformations in a similarity class, with Akansha Arora,  Linear Algebra and its Applications, 2021. arXiv

13. Splitting subspaces of linear operators over finite fields, with Divya Aggarwal, Finite Fields and Their Applications, 2022. arXiv 

14. Polynomial matrices, splitting subspaces and Krylov subspaces over finite fields, with Divya Aggarwal,  Finite Fields and Their Applications, 2022. arXiv 

15. Set partitions, tableaux, and subspace profiles of regular diagonal operators, with Amritanshu Prasad, Séminaire Lotharingien de Combinatoire, 2022 (Proceedings of FPSAC 2022, IISc Bangalore).

16. Generating functions for straight polyomino tilings of narrow rectangles, with Mudit Aggarwal, Journal of Integer Sequences, 2023. arXiv

17. Splitting subspaces and a finite field interpretation of the Touchard-Riordan formula, with Amritanshu Prasad, European Journal of Combinatorics, 2023. arXiv 

18. Enumeration of anti-invariant subspaces and Touchard's Formula for the entries of the q-Hermite Catalan matrix, with Amritanshu Prasad, Advances in Applied Mathematics, 2023. arXiv 

19. Set partitions, tableaux, and subspace profiles under regular diagonal matrices, with Amritanshu Prasad, European Journal of Combinatorics, 2024. arXiv 

20. Diagonal operators, q-Whittaker functions and rook theory, with Michael Schlosser, to appear in Combinatorial Theory. arXiv 

21. Subspace profiles over finite fields and q-Whittaker expansions of symmetric functions. arXiv 

22. Counting points on Hessenberg varieties over finite fields, with Alex Abreu and Antonio Nigro. arXiv 

23. Simple operators and q-Whittaker coefficients of power sum symmetric functions. arXiv 

24. Subspace profiles, q-Whittaker functions and Krylov methods, article 93B.115. (Proceedings of FPSAC 2025).

25. Counting Fq-points of orbital varieties in ad-nilpotent ideals of type An, with Mohammad Bardestani, Keivan Mallahi-Karai and Hadi Salmasian. arXiv

Some OEIS sequences pertaining to my research: A236581, A236580, A236579, A236576, A099390, A083066, A049086, A005710, A005709, A005708, A001835, A003269, A000930, A003520.