Research

Publications

1. Towards decidability of conjugacy of pairs and triples, with Benny George, Logic and its applications, Lecture Notes in Computer Science, 5378:224–231, Springer, Berlin, 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, 17(5):461–472, 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, 118(3):819–828, 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, 574:49–58, American Mathematical Society, 2012. arXiv

5. Arithmetic progressions in a unique factorization domain, with Sudhir Ghorpade, Acta Arithmetica, 54(2):161–171, 2012. arXiv

6. Enumeration of linear transformation shift registers, Designs, Codes and Cryptography, 75(2):301–314, 2015. arXiv

7. A new proof of Fitzgerald’s characterization of primitive polynomials, Finite Fields and Their Applications, 31(0):8–11, 2015. arXiv

8. Counting zero kernel pairs over a finite field, Linear Algebra and its Applications, 495:1–10, 2016. arXiv

9. The number of linear transformations defined on a subspace with given invariant factors, Linear Algebra and its Applications, 532:146–161, 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, pp. 25-61, 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, 625:196-211, 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, 86B, Article 35 (Proceedings of FPSAC 2022, IISc Bangalore).

16. Generating functions for straight polyomino tilings of narrow rectangles, with Mudit Aggarwal, Journal of Integer Sequences, Article 23.1.4, 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 

Preprints

1. Set partitions, tableaux, and subspace profiles under regular split semisimple matrices, with Amritanshu Prasad. arXiv 

2. Diagonal operators, q-Whittaker functions and rook theory, with Michael Schlosser. arXiv 

3. Subspace Profiles over Finite Fields and q-Whittaker expansions of symmetric functions. arXiv 

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