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
- A new statistic on Dyck paths for counting 3-dimensional Catalan words
Joint with Christina Graves. Accepted to Discrete Mathematics. arXiv:2205.09686.
- Enumerating two permutation classes by number of cycles
To appear in Discrete Mathematics and Theoretical Computer Science. arXiv:1803.08959.
- Pattern-restricted permutations composed of 3-cycles
Joint with Christina Graves. Discrete Mathematics, 345(7) (2022), 112895. arXiv:2104.12664.
- 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.
- Counting acyclic and strong digraphs by descents
Joint with Xuming Evans*, Ira Gessel, and Christina Graves. Discrete Mathematics, 343(11) (2020). arxiv:1909.01550.
- 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
- 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
- Classes of uniformly most reliable graphs for all-terminal reliability
Joint with Christina Graves and David Milan. Discrete Applied Mathematics, 267 (2019), 12-29.
- 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
- Rooted forests that avoid sets of permutations
Joint with Katie Anders. European Journal of Combinatorics, 77 (2019), 1-16. arxiv:1607.03046
- 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.
- Involutions and the Gelfand character
Joint with Virginia Germany**, C. Marin King*, and L.-K. Lauderdale. Preprint at arXiv:1804.02490.