My research interests lie in the areas of enumerative combinatorics and algebraic combinatorics. Most of my work so far has been in permutation enumeration and its connections to symmetric function theory and combinatorial Hopf algebras. In other words, I enjoy solving counting problems involving permutations and developing general frameworks for studying these kinds of problems, often drawing upon the rich interplay between combinatorics and abstract algebra.
Papers in Enumerative and Algebraic Combinatorics:- Shuffle-compatible descent statistics and quotients of quasisymmetric functions, with Ira M. Gessel. Sém. Lothar. Combin. 80B: Article #5, 12 pp., 2018.
- Shuffle-compatible permutation statistics, with Ira M. Gessel. Adv. Math. 332: 85-141, 2018.
- A generalized Goulden–Jackson cluster method and lattice path enumeration. Discrete Math. 341(2): 358-379, 2018.
- Eulerian polynomials and descent statistics. Adv. in Appl. Math. 90: 86–144, 2017.
- Counting permutations by runs. J. Combin. Theory Ser. A 142: 147–176, 2016.
- Counting permutations by alternating descents, with Ira M. Gessel. Electron. J. Combin. 21(4): Paper #P4.23, 21 pp., 2014.
As an undergraduate student, I did some work in extremal combinatorics. In addition to the two papers below, I wrote a (mostly expository) senior thesis on the model theory of random graphs. These are no longer research interests!
Papers in Extremal Combinatorics:- Logarithmic representability of integers as k-sums, with Anant P. Godbole, Samuel Gutekunst, and Vince Lyzinski. Integers 15A: Paper #A5, 14 pp., 2015.
- Shattering thresholds for random systems of sets, words, and permutations, with Anant P. Godbole and Samantha Pinella. Pure Math. Appl. (PU.M.A.) 24(2): 125–142, 2013.