Scholarship

My primary area of research and scholarship is Combinatorics. Specifically, algebraic and enumerative combinatorics as well as combinatorial number theory. I am also interested in graph theory.

Publication List

1. On the Genus of a quotient of a numerical semigroup, joint with S. Butler, C. Defant, Y. Gao, P. E. Harris, C. Hettle, Q. Liang, H. Nam and A. Volk, Semigroup Forum (2019). Published online Jan 3, 2019. DOI:https://doi.org/10.1007/s00233-018-9989-3.

2. Goncarov Polynomials in Partition Lattices and Exponential Families, joint with C. Yan. Advances in Applied Mathematics (2020) https://doi.org/10.1016/j.aam.2020.102045

3. Enumerating parking completions using Join and Split, joint with S. Butler, G. Dorpalen-Barry, P. E. Harris, C. Hettle, Q. Liang, J. L. Martin, and H. Nam. Electronic Journal of Combinatorics 27 (2), P2.44(2020). https://www.combinatorics.org/ojs/index.php/eljc/article/view/v27i2p44

4. Goncarov Polynomials, Partition Lattices and Parking Sequences, Ph.D Thesis, Texas A&M University (2020)

5. On increasing and invariant parking sequences, joint with C. Yan.  Austral. J. Combin. 79(1) (2021) https://arxiv.org/abs/2005.04759

6. Multivariate Difference Goncarov Polynomials, joint with L. Snider, and C. Yan. Integers, 21A (2021) #A1.

7. Pattern Avoidance in Parking Functions, joint with L. Pudwell. Enumer. Comb. Appl., 3(3): #S2R17, (2023).

In Preparation:

8. Pattern Avoidance in Parking Arrangements, joint with L. Pudwell. In preparation (2023).

9. On invariant and prime parking sequences, joint with V. Berger, R. Gong, M. G. Gonzalez, P. E. Harris, and A. Melendez. In preparation (2023).