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. As an algebraist, Professor McNicholas searches for symmetry in a wide variety of settings. In particular, she enjoys analyzing voting methods, cryptosystems, combinatorics, and graph theory through an algebraic lens. She is interested in courses and materials that integrate multiple mathematical perspectives, incorporate technology and applications, and generally humanize the subject. She co-authored the text Explorations in Number Theory - Commuting through the Numberverse and has developed courses on the history of mathematics and the design of escape rooms and mathematical puzzles. She has received teaching awards from the University of Arizona and Willamette University. In addition to her academic pursuits, Professor McNicholas enjoys painting and is a contributing artist for the second deck of EvenQuads playing cards, honoring notable women in mathematics.

Associate Dean for Faculty Development,

Professor of Mathematics

Department of Mathematics, Willamette University

Smullin 110

emcnicho@willamette.edu

503-370-6590

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Looking for something to do?

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

Announcements & Recent Publications:

[12] "Enumeration of interval-closed sets via Motzkin paths and quarter-plane walks" (Sergi Elizalde, Nadia Lafrenière, Joel Brewster Lewis, Erin McNicholas, Jessica Striker, and Amanda Welch) Journal of Combinatorics, Vol. 17 (4), pp 527-557, 2026.

In this paper, we advance the study of interval-closed sets of finite posets from an enumerative perspective, focusing on two important families: the product of two chain posets and truncated rectangle posets.

For the product of two chains, we derive an explicit generating function by constructing a bijection between interval-closed sets and certain bicolored Motzkin paths, a class of lattice paths with a well-understood combinatorial theory. This bijection illuminates the underlying structure of interval-closed sets and yields clean enumerative formulas as a result. For truncated rectangle posets, including type A root posets, we establish a functional equation for the generating function of interval-closed sets, again via a bijection, this time mapping to quarter-plane walks. Together, these results demonstrate that bijections to families of lattice paths provide a powerful and unifying toolkit for enumerating interval-closed sets across different poset families.

"Cyclic Sieving on Permutations - An Analysis of Maps and Statistics in the FindStat Database", Ashleigh Adams, J. Elder, N. LaFreniere, E. McNicholas, J. Striker, and A. Welch, Mathematics of Computation, December 12, 2025

In this work, we carry out the first systematic search for instances of the cyclic sieving phenomenon (CSP) on permutations using SageMath and the FindStat database. The cyclic sieving phenomenon occurs when a given polynomial, evaluated at certain roots of unity, gives the exact number of objects fixed by a specified cyclic group action; In other words, when a single polynomial encodes symmetry information about a set that is not at all obvious from the definitions alone.

Our results include 34 new instances of the CSP, and a clearer picture of how CSP compares with the related phenomenon of homomesy -- showing that, contrary to common expectations, the two do not always align.

This project builds on our earlier work and highlights the power of database-driven experimentation in discovering new structures in algebraic combinatorics.

"Voting on Relations Using Pairs Information", Karl-Dieter Crisman, Erin McNicholas, Kathryn L. Nyman, and Michael Orrison, Notices of the American Mathematical Society, Volume 72, Number 9, October 2025

From ranking movies on a streaming service to selecting job candidates or training machine learning models, we constantly face the challenge of combining many individual preferences into a single, collective decision. In this article, we present an elegant mathematical framework that unifies a wide array of these decision-making methods, known as aggregation procedures. By treating preferences not just as simple rankings but as complex relationships — allowing for ties, outright preference, or even incomparability — we use tools from linear algebra and graph theory to draw unexpected connections between seemingly disparate voting systems. This novel perspective can be used to create a "tunable" family of voting procedures, much like filters in signal processing, that can be adjusted to amplify or diminish specific aspects of voter preferences, shedding new light on how collective choices are made.

Last updated: 6/15/2026

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