**RESEARCH**

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The following is a list of research publications and preprints I have (co-)authored. Names marked with an asterisk (*) indicate undergraduate student co-authors.

- BFS versus DFS for random targets in ordered trees, with Stoyan Dimitrov and Martin Minchev. Submitted.
- Zig-zag Eulerian polynomials, with T. Kyle Petersen. Submitted.
- Two-sided permutation statistics via symmetric functions, with Ira M. Gessel. Submitted.
- A combinatorial proof of a tantalizing symmetry on Catalan objects, with Miklós Bóna, Stoyan Dimitrov, Gilbert Labelle, Yifei Li, Joseph Pappe, and Andrés R. Vindas Meléndez. Submitted.
- Statistics on clusters and
*r*-Stirling permutations, with Sergi Elizalde and Justin M. Troyka. To appear in*J. Comb.* - On the rix statistic and valley-hopping, with Nadia Lafrenière.
*Discrete Math. Theor. Comput. Sci.*26(2): Paper #3, 27 pp., 2024. - On kernels of descent statistics, with William L. Clark*.
*Electron. J. Combin.*31(2): Paper #P2.36, 33 pp., 2024. - A subfamily of skew Dyck paths related to
*k*-ary trees, with Yuxuan Zhang*.*J. Integer Seq.*27: Article 24.2.4, 22 pp., 2024. - Cyclic shuffle-compatibility via cyclic shuffle algebras, with Jinting Liang and Bruce E. Sagan.
*Ann. Comb.*28: 615–654, 2024. - Cyclic shuffle-compatibility and cyclic quasisymmetric functions, with Jinting Liang and Bruce E. Sagan. Proceedings of FPSAC 2023,
*Sém. Lothar. Combin.*89B: Article #41, 12 pp., 2023. - Fibonacci numbers, consecutive patterns, and inverse peaks, with Justin M. Troyka.
*Adv. in Appl. Math.*141: Article #102406, 19 pp., 2022. - Refined consecutive pattern enumeration via a generalized cluster method. Proceedings of FPSAC 2022,
*Sém. Lothar. Combin.*86B: Article #2, 12 pp., 2022. - A lifting of the Goulden–Jackson cluster method to the Malvenuto–Reutenauer algebra.
*Algebr. Comb.*5(6): 1391–1425, 2022. - Plethystic formulas for permutation enumeration, with Ira M. Gessel.
*Adv. Math.*375: Article #107370, 55 pp., 2020. - Counting permutations by peaks, descents, and cycle type, with Ira M. Gessel. Proceedings of FPSAC 2020,
*Sém. Lothar. Combin.*84B: Article #12, 12 pp., 2020. - On the joint distribution of cyclic valleys and excedances over conjugacy classes of 𝕾
_{n}, with M. Crossan Cooper* and William S. Jones*.*Adv. in Appl. Math.*115: Article #101999, 15 pp., 2020. - Hopping from Chebyshev polynomials to permutation statistics, with Jordan O. Tirrell.
*Electron. J. Combin.*26(3): Paper #P3.27, 17 pp., 2019. - Homomorphisms on noncommutative symmetric functions and permutation enumeration, with Ira M. Gessel. Proceedings of FPSAC 2019,
*Sém. Lothar. Combin.*82B: Article #6, 12 pp., 2019. - Shuffle-compatible descent statistics and quotients of quasisymmetric functions, with Ira M. Gessel. Proceedings of FPSAC 2018,
*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. - Logarithmic representability of integers as
*k*-sums, with Anant P. Godbole, Samuel Gutekunst, and Vince Lyzinski. Proceedings of Integers 2013: The Erdős Centennial Conference,*Integers*15A: Paper #A5, 15 pp., 2015. - Counting permutations by alternating descents, with Ira M. Gessel.
*Electron. J. Combin.*21(4): Paper #P4.23, 21 pp., 2014. - Shattering thresholds for random systems of sets, words, and permutations, with Anant P. Godbole and Samantha Pinella. Proceedings of Permutation Patterns 2012,
*Pure Math. Appl. (PU.M.A.)*24(2): 125–142, 2013.