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
- Enumeration of cyclic permutations in vector grid classes
Joint with L.-K. Lauderdale. Accepted to Journal of Combinatorics.
- Unimodal permutations and almost-increasing cycles
Joint with L.-K. Lauderdale. Electronic Journal of Combinatorics, 24(3) (2017), #P3.36. Link.
- 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
- Characterization of the allowed patterns of signed shifts
Discrete Applied Mathematics, 217(2) (2017), 97–109. arXiv:1506.03464
- Descents of λ-unimodal cycles in a character formula
Discrete Mathematics, 339 (2016), 2399–2409. arXiv:1401.2433
- Cyclic permutations realized by signed shifts
Joint with Sergi Elizalde. Journal of Combinatorics, 5 (2014), 1–30. arXiv:1304.7790
Peer-Reviewed Conference Proceedings:
- 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.
- Patterns of negative shifts and signed shifts
Joint with Sergi Elizalde and Katherine Moore. Séminaire Lotharingien de Combinatoire, 78B.49 (2017), 12 pp.
- Descents of λ-unimodal cyclic permutations (Extended Abstract)
Discrete Mathematics and Theoretical Computer Science proceedings AS, (2014), 417–428.
- Periodic patterns of signed shifts (Extended Abstract)
Joint with Sergi Elizalde. Discrete Mathematics and Theoretical Computer Science proceedings AS, (2013), 873–884.
- Rooted forests that avoid sets of permutations
Joint with Katie Anders. Preprint at arXiv:1607.03046.
- Classes of uniformly most reliable graphs for all terminal reliability
Joint with Christina Graves and David Milan.
- On the number of cycles in Av(312,4321) and Av(321,4123)
Preprint at arXiv:1803.08959.
- Involutions and the Gelfand characterJoint with Virginia Germany**, C. Marin King*, and L.-K. Lauderdale. Preprint at arXiv:1804.02490.
- Pattern restricted quasi-Stirling permutations
Joint with Adam Gregory*, Bryan Pennington*, and Stephanie Slayden*. Preprint at arXiv:1804.07267.
- 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.