RESEARCH PUBLICATIONS

Published Papers

1. Combinatorial properties of Rogers-Ramanujan-type identities arising from Hall-Littlewood polynomials (with Claire Frechette).  Annals of Combinatorics 20: 2 (2016), 345-360.

2. Congruences for powers of the partition function (with Ian Wagner).  Annals of Combinatorics 21: 1 (2017), 83-93.

3. Shifted distinct-part partition identities in arithmetic progressions (with Ethan Alwaise, Robert Dicks, Jason Friedman, Lianyan Gu, Zach Harner, Hannah Larson, Ian Wagner, and Josh Weinstock).  Annals of Combinatorics 21: 4 (2017), 479-494.

4. Conjugacy growth series for finitary wreath products.  Research in Number Theory 3: 7 (2017).

5. A new formula for Chebotarev densities.  Research in Number Theory 3: 27 (2017).

6. Effective bounds for the Andrews spt-function (with Riad Masri).  Forum Mathematicum, Volume 31, Issue 3 (2019), 743-767.

7. Multiquadratic fields generated by characters of An (with Ken Ono and Ian Wagner).  Journal of Algebra, Volume 533 (2019), 339-343.

8. Higher Width Moonshine (with Ken Ono).  Advances in Mathematics, Volume 360 (2020), doi.org/10.1016/j.aim.2019.106896.

9. Fields generated by characters of finite linear groups (with Ken Ono and Ian Wagner).  Archiv der Mathematik 116 (2021), 487-500.

10. Generalized Paley graphs and their complete subgraphs of orders three and four (with Dermot McCarthy).  Research in the Mathematical Sciences, 8: 18 (2021), doi.org/10.1007/s40687-021-00254-7.

11. Self-conjugate t-core partitions and applications (with Benjamin Sharp).  Australasian Journal of Combinatorics 82(2) (2022), 212-227.

12. Derivatives and Integrals of Polynomials Associated with Integer Partitions (with Tyler Russell and Dannie Urban).  Journal of Integer Sequences 25 (2022), Article 25.5.1.

13. A “supernormal” partition statistic (with Robert Schneider and Matt Just). Journal of Number Theory 241 (2022), 120-141.

14. Bijections, generalizations, and other properties of sequentially congruent partitions (with Ezekiel Cochran, Emma Harrell, and Samuel Saunders). Ramanujan Journal (2023), https://doi.org/10.1007/s11139-023-00728-y.

15. Representations of integers as quotients of sums of distinct powers of three (with Katie Anders, Bruce Reznick, and Simone Sisneros-Thiry).  Submitted.

16. Non-standard binary representations and the Stern sequence (with Katie Anders, Rajat Gupta, and Joseph Vandehey).  Accepted in Electronic Journal of Combinatorics.

17. Inequalities and asymptotics for hook numbers in restricted partitions (with Will Craig and Guo-niu Han).  Submitted.

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Papers in Progress​

1. Summation formulas in the theory of Hecke's functional equation (with Rajat Gupta).  In preparation.

2. Non-standard quaternary representations and the Fibonacci numbers (with Katie Anders, Rajat Gupta, Noah Lebowitz-Lockard, and Joseph Vandehey).  In preparation.

3. Combinatorial properties of standard Young tableaux and their relationship to permutations (with Millie Jeske, Alessandra Martinez, Alessandro Russo, and Mat Taylor). In preparation.

4. Digraphs for quotients of sums of distinct powers of three (with Katie Anders, Bruce Reznick, and Simone Sisneros-Thiry).  In preparation.

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Conference Proceedings

1. CM evaluations of the Goswami-Sun series (with Ken Ono). Proceedings of Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory. Zeuthen, Germany (2017). Texts & Monographs in Symbolic Computation. Eds. J. Blümlein, C. Schneider, and P. Paule. Springer Nature Switzerland AG (2019), 183-193.

2. Hypergeometric Functions over Finite Fields and Modular Forms: A Survey and New Conjectures (with Dermot McCarthy).  From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory. Eds. F. Gesztesy and A. Martinez-Finkelshtein.  Operator Theory: Advances and Applications, Volume 285. Birkhäuser, Springer Nature Switzerland AG (2021), 41-56.

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Book Chapters

1. Review of "Your hit parade: the top ten most fascinating formulas in Ramanujan's lost notebook," by B. C. Berndt and G. E. Andrews.  Encyclopedia of Srinivasa Ramanujan and His Mathematics.  Submitted.

2. Ramanujan and the Nekrasov-Okounkov Formula.  Encyclopedia of Srinivasa Ramanujan and His Mathematics.  Submitted.

OTHER PUBLICATIONS

1. Popular magazine article: Speed Seeking (with Ken Ono). Splash Magazine (Summer 2019), 38-39.