# Erin McNicholas

Dr. Erin McNicholas is a full professor of mathematics at Willamette University. Before receiving her Ph.D. from the University of Arizona she worked for the State of Oregon as a Metrologist and for the cryptography group at Sandia National Laboratory. Her research interests include Algebraic Combinatorics, Algebraic Voting Theory, Graph Theory, and Cryptography. She has received teaching awards from Willamette University and the University of Arizona and has developed courses and materials that integrate multiple mathematical perspectives and integrate inquiry based pedagogy. As part of this work, she co-authored the textbook Explorations in Number Theory: Commuting through the Numberverse. She also enjoys painting and contributed artwork for Deck 2 of the Association for Women in Mathematics EvenQuads playing cards.

### Professor of Mathematics

Ford Hall 211

900 State St

Salem, Oregon 97301

503-370-6590

### Office Hours, Spring '24

Check calendar below for updates

Monday 3-4 pm

Tuesday 11:15am-12:15 pm

Thursday: 4-5 pm

*While these are the default times and you don't need an appointment, please check the calendar below for any changes. Office hours are cancelled on University holidays. Additional times are available by appointment. You can also post questions on the course channel of the WU Math discord server.

### Looking for something to do?

Attend an upcoming Math Colloquium

Check out other opportunities and fun things to do on my Opportunities & Community page, including opportunities for paid summer math research

### Announcements & Recent Publications:

Approval Gap of Weighted k-Majority Tournaments by J. Coste, B. Flesch, J. Laison, E. McNicholas, and D. Miyata now available from Theory and Applications of Graphs Vol 11, Iss 1 Article 3 (2024)

Lying at the intersection of graph theory and voting theory, a k-majority tournament is a direct graph whose vertices are the set of candidates or choices given to voters. An edge is drawn from candidate u to candidate v if and only if they are preferred by at least k of the voters, where k is some set value greater than half the size of the electorate. In a weighted k-majority tournament, each edge is labeled with the number of voters preferring u to v. In this paper we define a measure (the approval gap) for how strongly a dominating set in such a tournament beats the next most popular candidate. We prove upper and lower bounds on the approval gap, and construct tournaments having a specified approval gap within a given range dependent on k.

Homomesies on permutations: An analysis of maps and statistics in the FindStat database by J. Elder, N Lafrenière, Erin McNicholas, Jessica Striker, Amanda Welch is now available from the Mathematics of Computation (2023)

In this paper, we perform a systematic study of permutation statistics and bijective maps on permutations in which we identify and prove 122 instances of the homomesy phenomenon. Homomesy occurs when the average value of a statistic is the same on each orbit of a given map. The maps we investigate include the Lehmer code rotation, the reverse, the complement, the Foata bijection, and the Kreweras complement. The statistics studied relate to familiar notions such as inversions, descents, and permutation patterns, and also more obscure constructs. Besides the many new homomesy results, we discuss our research method, in which we used SageMath to search the FindStat combinatorial statistics database to identify potential homomesies.

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.

Last updated: 5/3/24