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.

  1. Desarrangements revisited: statistics and pattern avoidance, with Chadi Bsila*, Caroline E. Cox*, Anna S. Hugo*, and Lindsey A. Styron*. Submitted.
  2. Counting pattern-avoiding permutations by big descents, with Sergi Elizalde and Johnny Rivera, Jr.* Submitted.
  3. BFS versus DFS for random targets in ordered trees, with Stoyan Dimitrov and Martin Minchev. Submitted.
  4. 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.
  5. Two-sided permutation statistics via symmetric functions, with Ira M. Gessel. To appear in Forum Math. Sigma.
  6. Zig-zag Eulerian polynomials, with T. Kyle Petersen. European J. Combin. 124: Article #104073, 30 pp., 2025.
  7. On the rix statistic and valley-hopping, with Nadia Lafrenière. Discrete Math. Theor. Comput. Sci. 26(2): Paper #3, 27 pp., 2024.
  8. On kernels of descent statistics, with William L. Clark*. Electron. J. Combin. 31(2): Paper #P2.36, 33 pp., 2024.
  9. 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.
  10. Cyclic shuffle-compatibility via cyclic shuffle algebras, with Jinting Liang and Bruce E. Sagan. Ann. Comb. 28: 615–654, 2024.
  11. Statistics on clusters and r-Stirling permutations, with Sergi Elizalde and Justin M. Troyka. J. Comb. 15(3): 319–359, 2024.
  12. 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.
  13. Fibonacci numbers, consecutive patterns, and inverse peaks, with Justin M. Troyka. Adv. in Appl. Math. 141: Article #102406, 19 pp., 2022.
  14. Refined consecutive pattern enumeration via a generalized cluster method. Proceedings of FPSAC 2022, Sém. Lothar. Combin. 86B: Article #2, 12 pp., 2022.
  15. A lifting of the Goulden–Jackson cluster method to the Malvenuto–Reutenauer algebra. Algebr. Comb. 5(6): 1391–1425, 2022.
  16. Plethystic formulas for permutation enumeration, with Ira M. Gessel. Adv. Math. 375: Article #107370, 55 pp., 2020.
  17. 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.
  18. On the joint distribution of cyclic valleys and excedances over conjugacy classes of 𝕾n , with M. Crossan Cooper* and William S. Jones*. Adv. in Appl. Math. 115: Article #101999, 15 pp., 2020.
  19. Hopping from Chebyshev polynomials to permutation statistics, with Jordan O. Tirrell. Electron. J. Combin. 26(3): Paper #P3.27, 17 pp., 2019.
  20. 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.
  21. 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.
  22. Shuffle-compatible permutation statistics, with Ira M. Gessel. Adv. Math. 332: 85–141, 2018.
  23. A generalized Goulden–Jackson cluster method and lattice path enumeration. Discrete Math. 341(2): 358–379, 2018.
  24. Eulerian polynomials and descent statistics. Adv. in Appl. Math. 90: 86–144, 2017.
  25. Counting permutations by runs. J. Combin. Theory Ser. A 142: 147–176, 2016.
  26. 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.
  27. Counting permutations by alternating descents, with Ira M. Gessel. Electron. J. Combin. 21(4): Paper #P4.23, 21 pp., 2014.
  28. 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.

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