Research
Research Interests
Algebraic Combinatorics, Representation Theory, Algebraic Voting Theory, Algebraic & Spectral Graph Theory, and Cryptography
CV: http://willamette.edu/~emcnicho/cv-mcnicholas.pdf
Copies of select papers available: Erin McNicholas - Google Scholar, Erin McNicholas - ResearchGate
Books & Edited Volumes
I'm excited to announce the publication of Explorations in Number Theory: Commuting through the Numberverse, with coauthors Cam McLeman and Colin Starr. Quoting from the Springer website,
This innovative undergraduate textbook approaches number theory through the lens of abstract algebra. Written in an engaging and whimsical style, this text will introduce students to rings, groups, fields, and other algebraic structures as they discover the key concepts of elementary number theory. Inquiry-based learning (IBL) appears throughout the chapters, allowing students to develop insights for upcoming sections while simultaneously strengthening their understanding of previously covered topics.
Book Chapters
"Matroids" (with C. Starr and N. Neudauer), chapter in A Primer for Undergraduate Research : From Groups and Tiles to Frames and Vaccines, Foundations for Undergraduate Research in Mathematics, Editors : C. Lee, V. Peterson, and A. Wootton, Birkhäuser (2018)
"Group Examinations in Introduction-to-Proof Courses" (with I. Johnson), chapter in Beyond Lecture: Techniques to Improve Student Proof-Writing Across the Curriculum, MAA Press, Editors: R. Schwell, A. Steurer, J. Vasquez (2016)
Peer-reviewed Journal Articles
"Approval Gap of Weighted k-Majority Tournaments" (with J. Coste*, B. Flesch, J. Laison, and D. Miyata*), Theory and Applications of Graphs Vol 11, Iss. 1 (2024)
"Toggling, Rowmotion, and Homomesy on Interval-Closed Sets" (J. Elder, N. LaFreniere, E. McNicholas, J. Striker, A. Welch), accepted for publication in the Journal of Combinatorics (2023)
"Homomesies on permutations: An analysis of maps and statistics in the FindStat database" (with J. Elder, N. Lafrenière, J. Striker, and A. Welch), Mathematics of Computation (2023).
"Algebraic Voting Theory & Representations of $S_m\wr S_n$" (with H. Barcelo, M. Bernstein, S. Bockting-Conrad, K. Nyman, and S. Viel), Advances in Applied Mathematics, Volume 120, September 2020, 102077
"Base Size Sets and Determining Sets" (with J. Laison and N. Seaders), Discrete Mathematics, Vol. 342(11), (November 2019) pp. 2994-2999
"Unipancyclic Matroids" (with W. Agnew-Svoboda*, A. Huszar*, J. Schreiner-McGraw*, C. Starr, and C. Yap*), Discrete Mathematics, Vol. 342(8), (August 2019) pp. 2254-2269
"Graph Invertibility" (with C. McLeman). Graphs and Combinatorics Vol 30(4), (2014) pp. 977-1002
"Eigenvalue Statistics of One-Face Maps." Congressus Numerantium, Vol. 207-211, (2011)
"Spectra of Coronae" (with C. McLeman). Linear Algebra and Its Applications Vol 435(5) (2011) pp. 998-1007
*denotes an undergraduate co-author.
Works in Progress
"Cyclic Sieving on Permutations - An Analysis of Maps an Statistics in the FindStat Database" (Ashleigh Adams, J. Elder, N. LaFreniere, E. McNicholas, J. Striker, and A. Welch) https://arxiv.org/abs/2402.16251
"Voting on Relations Using Pairs Information" (K.-D. Crisman, E. McNicholas, K. Nyman, and M. Orrison) currently under review
Interval Closed Sets on Posets ( N. LaFreniere, J. Lewins, E. McNicholas, J. Striker, and A. Welch)
Research Connections: A celebration of work by affiliates of Carleton College's Summer Mathematics Program (ed.s A. Brisbin, K. Lange, E. McNicholas, E. Purvine), https://sites.google.com/willamette.edu/smpvolume/home
Mountain Graphs (with B. Flesch, J. Laison, and A. Wright)
Ph.D. in Applied Mathematics
Embedded Tree Structures and Eigenvalue Statistics of Genus Zero One-Face Maps,
from the University of Arizona , under the direction of Hermann Flaschka
Last updated 1/30/2024