Research

My research is primarily in enumerative combinatorics. A list of publications can be seen below. I’m also excited about undergraduate research. Click here for more information about my work with undergraduates.


LIST OF PUBLICATIONS

Accepted/Appeared:

  1. Enumeration of cyclic permutations in vector grid classes
    Joint with L.-K. Lauderdale. Accepted to Journal of Combinatorics.
  2. Unimodal permutations and almost-increasing cycles
    Joint with L.-K. Lauderdale. Electronic Journal of Combinatorics, 24(3) (2017), #P3.36. Link.
  3. 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
  4. Characterization of the allowed patterns of signed shifts
    Discrete Applied Mathematics, 217(2) (2017), 97–109. arXiv:1506.03464
  5. Descents of λ-unimodal cycles in a character formula
    Discrete Mathematics, 339 (2016), 2399–2409. arXiv:1401.2433
  6. 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. Rooted forests that avoid sets of permutations
    Joint with Katie Anders. Preprint at arXiv:1607.03046.
  2. Classes of uniformly most reliable graphs for all terminal reliability
    Joint with Christina Graves and David Milan.
  3. On the number of cycles in Av(312,4321) and Av(321,4123)
    Preprint at arXiv:1803.08959.
  4. Involutions and the Gelfand characterJoint with Virginia Germany**, C. Marin King*, and L.-K. Lauderdale. Preprint at arXiv:1804.02490.
  5. Pattern restricted quasi-Stirling permutations
    Joint with Adam Gregory*, Bryan Pennington*, and Stephanie Slayden*. Preprint at arXiv:1804.07267.
  6. 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**. Preprint available upon request.

I also have a few projects in progress, including papers with students.