Research

My research is primarily in enumerative combinatorics. A list of publications can be seen below. (A * indicates an undergraduate co-author and a ** indicated a graduate student co-author.)

LIST OF PUBLICATIONS

Accepted/Appeared:

  1. A new statistic on Dyck paths for counting 3-dimensional Catalan words 
    Joint with Christina Graves. Accepted to Discrete Mathematics. arXiv:2205.09686.
  2. Enumerating two permutation classes by number of cycles
    To appear in Discrete Mathematics and Theoretical Computer Science. arXiv:1803.08959.
  3. Pattern-restricted permutations composed of 3-cycles
    Joint with Christina Graves. Discrete Mathematics, 345(7) (2022), 112895. arXiv:2104.12664.
  4. Vertex-minimal planar graphs with cyclic 2-group symmetry
    Joint with Rebecca Darby**, L.-K. Lauderdale, Asa Linson*, Mariah K. Maxfield*, Charles Schmidt*, and Phung Tran**. Journal of Algebraic Combinatorics, 54 (2021). 1-15.
  5. Counting acyclic and strong digraphs by descents
    Joint with Xuming Evans*, Ira Gessel, and Christina Graves. Discrete Mathematics, 343(11) (2020). arxiv:1909.01550.
  6. Arithmetical structures on bidents
    Joint with Abigail C. Bishop, Alexander Diaz-Lopez, Luis D. García Puente, Darren Glass, and Joel Louwsma. Discrete Mathematics, 343(7) (2020), 111850. arxiv:1903.01393
  7. Enumeration of cyclic permutations in vector grid classes
    Joint with L.-K. Lauderdale. Journal of Combinatorics, 11(1) (2020), 203-230. arxiv.org:1606.04502
  8. Classes of uniformly most reliable graphs for all-terminal reliability
    Joint with Christina Graves and David Milan. Discrete Applied Mathematics, 267 (2019), 12-29.
  9. Pattern-restricted quasi-Stirling permutations
    Joint with Adam Gregory*, Bryan Pennington*, and Stephanie Slayden*. Australasian Journal of Combinatorics, 74(3) (2019), 389-407. arxiv.org:1804.07267
  10. Rooted forests that avoid sets of permutations
    Joint with Katie Anders. European Journal of Combinatorics, 77 (2019), 1-16. arxiv:1607.03046
  11. Unimodal permutations and almost-increasing cycles
    Joint with L.-K. Lauderdale. Electronic Journal of Combinatorics, 24(3) (2017), #P3.36. Link.
  12. Allowed patterns of symmetric tent maps via commuter functions
    Joint with Scott M. LaLonde. SIAM Journal of Discrete Mathematics, 31(1) (2017), 317-334. arXiv:1606.01317
  13. Characterization of the allowed patterns of signed shifts
    Discrete Applied Mathematics, 217(2) (2017), 97-109. arXiv:1506.03464
  14. Descents of λ-unimodal cycles in a character formula
    Discrete Mathematics, 339 (2016), 2399-2409. arXiv:1401.2433
  15. Cyclic permutations realized by signed shifts 
    Joint with Sergi Elizalde. Journal of Combinatorics, 5 (2014), 1-30. arXiv:1304.7790

Peer-Reviewed Conference Proceedings:

  1. On the number of λ-unimodal involutions (Extended Abstract)
    Joint with Angela M. Gay, Virginia Germany, C. Marin King, L.-K. Lauderdale, Thomas Lupo, and F. L. Rossi. Séminaire Lotharingien de Combinatoire, 80B.66 (2018), 12 pp.
  2. Patterns of negative shifts and signed shifts
    Joint with Sergi Elizalde and Katherine Moore. Séminaire Lotharingien de Combinatoire, 78B.49 (2017), 12 pp.
  3. Descents of λ-unimodal cyclic permutations (Extended Abstract)
    Discrete Mathematics and Theoretical Computer Science proceedings AS, (2014), 417–428.
  4. Periodic patterns of signed shifts (Extended Abstract)
    Joint with Sergi Elizalde. Discrete Mathematics and Theoretical Computer Science proceedings AS, (2013), 873–884.

Submitted:

  1. Involutions and the Gelfand character
    Joint with Virginia Germany**, C. Marin King*, and L.-K. Lauderdale. Preprint at arXiv:1804.02490.