#### Participant Quotes

- I was able to learn about open and accessible problems for undergraduates in graph theory, and I have begun my own research in the area to enhance my knowledge and skills when working with undergraduates. I know of no other opportunity like REUF where one can learn the basics of a new research area and even be given open questions accessible to undergraduates.
- Meeting faculty in similar situations as me has been the most beneficial. I like knowing a network of people to keep in touch with.
- I feel re-energized as a mathematician. The possibilities for my own as well as student research have far exceeded my expectations. The multitude and variety of collaborations has been wonderful.
*I have greatly benefited from the variety of problems described, the discussion on the logistics of running an undergraduate research program, and the camaraderie, with other liberal arts faculty. This has been easily been the most worthwhile workshop or conference I’ve ever attended.*

## Undergraduate and Faculty Research Outcomes

A high proportion of faculty from each REUF workshop go on to mentor undergraduate researchers, and many faculty also continue collaborating with fellow faculty workshop participants and mathematical leaders. Outcomes are tracked for two years after each workshop, starting a year after the workshop.

**Faculty participants:** 221 faculty from more than 100 primarily undergraduate institutions have participated in a REUF workshop since 2008.

**Student research:** 390 undergraduate students were mentored by REUF alumni in research. Collectively, the students made 277 presentations, completed 22 honors theses, and co-authored 9 publications. Thirty-four student-faculty collaborations received other grant funding. Several students were accepted to off-site NSF REU programs, and one won first prize for a presentation at a national meeting.

**Faculty research:** Ninety-one undergraduate faculty were involved in new collaborations with other faculty. More than 20 small research groups met for an additional week with support from the REUF program. All together, their research has resulted in 77 presentations and 51 research articles in various stages of publication, some with student co-authors.

**Other notable outcomes:**

- Special sessions at the Joint Mathematics Meetings organized by REUF alumni
- Development of new undergraduate courses on REUF research topics
- Departmental changes such as the creation of a for-credit undergraduate research seminar for math majors

## Research Publications

*Peer-reviewed journal articles resulting from research begun at REUF workshops.*

#### REUF 2019

Alvarado, R., Averett, M., Gaines, B., Jackson, C., Karker, M. L., Marciniak, A., Su, F., & Walker, S. The Game of Cycles. To Appear, *American Mathematical Monthly*. https://arxiv.org/abs/2004.00776.

Ardila, R., Caples, C., Grundman, H. G., Hall-Seelig, L. L., Jordan, J. E., Kohl, K. T., & Wakefield, T. P. Values of Weighted Davenport Constants. To Appear, *Integers, 21*.

Jones, B., Kochalski, K. D., Loeb, S., Walk, J. C. Strategy-Indifferent Games of Best Choice. To Appear, *Discrete Mathematics*. https://arxiv.org/abs/2107.04872

#### REUF 2018

Ansaldi, K., El-Turkey, H., Hamm, J. Nu’Man, A., Warnberg, N., & Young, M. (2020). Rainbow Numbers of Z_n for a_1 x_1 + a_2 x_2 + a_3 x_3 = b. *Integers, 20*, A51.

Davis, T. C., De Lamere, A. Sopena, G., Soto, R. C., Vyas, S., & Wong, M. (2021). Peg solitaire in 3 colors on graphs. *Involve, 13*.

Davis, T.C., Grimley, L., Ince, K., Karaali, G., Kostadinov, B., & Soto, R.C. From Puzzles to Proof-writing: Exploring Rich Mathematical Ideas through Mechanical Puzzles. To Appear in *Teaching Mathematics Through Games* (MAA).

Ledder, G., Rebarber, R., Pendleton, T., Laubmeier, A.N., & Weisbrod, J. (2021). A discrete/continuous time resource competition model and its implications. *Journal of Biological Dynamics, 15*, S168–S189.

#### REUF 2017

Anders, K., Crans, A., Foster-Greenwood, B., Mellor, B., Tymoczko, J. (2020). Graphs admitting only constant splines. *Pacific Journal of Mathematics, 304*(2), 385-400.

Archer, K., Bishop, A., Diaz-Lopez, A., Garcia Puente, L.D., Glass, D., Louwsma, J. (2020). Arithmetical structures on bidents. *Discrete Mathematics, 343*(7), 111850 (23 pp).

Harris, Z. & Louwsma, J. (2020). On arithmetical structures on Complete Graphs. *Involve, 13*(2), 345-355.

#### REUF 2016

Asplund, J., Edoh, K., Haas, R., Hristova, Y., Novick, B., Werner, B. (2018). Reconfiguration graphs of shortest paths. *Discrete Mathematics, 341*, 2938-2948.

Asplund, J. & Werner, B. Classification of Reconfiguration Graphs of Shortest Path Graphs With No Induced 4-cycles. (2020). *Discrete Mathematics, 343*(1), 111640 (9pp).

Benesh, B., Carter, J., Coleman, D. A., Crabill, D. G., Good, J. H., Smith, M. A., Travis, J., & Ward, M. D. (2018). Periods in Subtraction Games, in *29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)*, 8:1–8:3.

Collins, J. B., Haas, R., Helminck, A. G., Lenarz, J., Pelatt, K. E., Saccon, S., & Welz, M. (2020). Extended symmetric spaces and 0-twisted involution graphs. *Communications in Algebra, 48*(6), 2293-2306.

#### REUF 2015

Benson, K. F., Ferrero, D., Flagg, M., Furst, V., Hogben, L., Vasilevska, V., & Wissman, B. (2018). Power domination and zero forcing. *Australasian Journal of Combinatorics, 70*, 221-235. Available at http://arxiv.org/abs/1510.02421.

Benson, K. F., Ferrero, D., Flagg, M., Furst, V., Hogben, L., & Vasilevska, V. (2018). Note on Nordhaus-Gaddum problems for power domination. *Discrete Applied Mathematics, 251*, 103-113.

Elliott, S., Lewis, A., Steinfeld, A., Zollinger, E., & Köse, E. (2019). Modeling the stem-cell hypothesis. *Mathematical Biosciences and Engineering, 16*.

Köse, E., Moore, S., Ofodile, C., Radunskaya, A., Swanson, E. R., & Zollinger, E. (2017). Immuno-kinetics of immunotherapy: Dosing with DCs. *Letters in Biomathematics, 4*, 39-58.

Ledder, G., Sylvester, D., Bouchat, R., & Thiel, J. (2018). *Mathematical Biosciences and Engineering, 15*, 841-862.

#### REUF 2014

Baker Swart, B, Beck, K., Crook, S., Eubanks-Turner, C., Grundman, H., Mei, M., & Zack, L. (2017). Augmented generalized happy functions. *Rocky Mountain Journal of Mathematics, 47*, 403-417.

Baker Swart, B., Beck, K., Crook, S., Eubanks-Turner, C., Grundman, H., Mei, M., & Zack, L. (2018). Augmented generalized happy functions. *Rocky Mountain Journal of Mathematics, 48*, 47-58.

Baker Swart, B., Hall-Seelig, L., Crook, S., Mei, M., Grundman, H. G., & Zack, L. (2014). Fixed points of augmented generalized happy functions II: Oases and mirages. *Journal of Integer Sequences, 22*.

Baker Swart, B., & Harbol, M. (2015). Augmented Happy Functions of Higher Powers. *Journal of the South Carolina Academy of Science, 13*(2), Article 7.

Catral, M., Ford, P., Harris, P., Miller, S. J., Nelson, D., Pan, Z., & Xu, H. (2017). New behavior in legal decompositions arising from non-positive linear recurrences. *Fibonacci Quarterly, 55*(3), 252-275.

Catral, M., Ford, P., Harris, P., Miller, S. J., & Nelson, D. (2016). Legal decomposition arising from non-positive linear recurrences. *Fibonacci Quarterly, 54*(4), 348-365.

Catral, M., Ford, P., Harris, P., Miller, S. J., & Nelson, D. (2014). Generalizing Zeckendorf’s Theorem: The Kentucky Sequence. *Fibonacci Quarterly, 52*(5), 68-90.

Dorward, R., Ford, P., Fourakis, E., Harris, P. E., Miller, S. J., Palsson, Eyvi, & Paugh, H. (2017). A generalization of Zeckendorf’s Theorem via circumscribed *m*-gons. *Involve, 19*, 125-150.

Dorward, R., Ford, P., Fourakis, E., Harris, P. E., Miller, S. J., Palsson, Eyvi, & Paugh, H. (2017). Individual gap measures from generalized Zeckendorf decompositions. *Uniform Distribution Theory, 12*, 27-36.

Grundman, H., & Harris, P. (2018). Sequences of consecutive happy numbers in negative bases. *Fibonacci Quarterly, 56,* 221-228.

Mei, M., & Read-McFarland, A. (2018). Numbers and the heights of their happiness. *Involve, 11*(2), 235-241.

#### REUF 2013

Beier, J., Fierson, J., Haas, R., Russell, H., & Shavo, K. (2016). Classifying coloring graphs. *Discrete Math, 339*(8), 2100-2112.

Buell, C., Klima, V., Schaefer, J., Wright, C., & Ziliak, E. (2018). Orbit decompositions of of unipotent elements in the generalized symmetric spaces of SL_2(Fq_). *Advances in the Mathematical Sciences, Association for Women in Mathematics, 15*, 69-77.

Buell, C., Helminck, A., Klima, V., Schaefer, J., Wright, C., & Ziliak, E. (2020). Classifying the orbits of the generalized symmetric spaces for SL_2(Fq_). *Communications in Algebra, 48*(4), 1744-1757.

Buell, C., Helminck, A., Klima, V., Schaefer, J., Wright, C., & Ziliak, E. (2017). On the structure of generalized symmetric spaces of SL_n(F_q). *Communications in Algebra, 45*, 5123-5136.

Buell, C., Helminck, A., Klima, V., Schaefer, J., Wright, C., & Ziliak, E. (2017). On the structure of generalized symmetric spaces of SL_2(F_q) and GL_2(F_q). *Note di Matematica, 37*, 1-10.

Callahan, J., Eager, E., Rebarber, R., Strawbridge, E., & Yuan, S. (2019). Analysis of a length-structured model for fish. *Bulletin of Mathematical Biology, 81,* 3732-3752.

Callahan, J., Rebarber, R., Strawbridge, E., & Yuan, S. (2015). Analysis of a coupled, *n*-patch population model with density dependence. *International Journal of Difference Equations, 10*, 137-159.

Schaefer, J., & Schlechtweg, K. (2017). On the structure of symmetric spaces of the semihedral groups. *Involve, 10*, 665-676.

#### REUF 2012

Ansill, T., Jacob, B., Penzellna, J., & Saavedra, D. (2016). Failed skew zero forcing on a graph. *Linear Algebra and Its Applications, 509*, 40-63.

Ansill, T., Jacob, B., Podlisny, B., Saavedra, D., & Yeung, P. (2015). Three-state zero forcing on graphs. *Congressus Numerantium, 225,* 73-81.

Berliner, A., Dean, N., Hook, J., Marr, A., Mbirika, A., & McBee, C. D. (2016). Coprime and prime labelings of graphs. *Journal of Integer Sequences, 19*(16.5.8).

Fetcie, K., Jacob, B, & Saavedra, D. (2015). The failed zero forcing number of a graph. *Involve, 8*(1), 99-117.

Grood, C., Harmse, J.A., Hogben, L., Hunter, T., Jacob, B., Klimas, A., McCathern, S. (2014). Minimum rank of zero-diagonal matrices described by a graph. *Electronic Journal of Linear Algebra, 27*, 458-477.

#### REUF 2011

Camenga, K. A., Collins, B., Hoefer, G., Quezada, J., Rault, P. X., Willson, J., & Yates, R. B. J. (2021). On the geometry of numerical ranges over finite fields. *Linear Algebra and Its Applications, 628*, 182-201.

Camenga, K. A., Deaett, L., Rault, P. X., Sendova, T., Spitkovsky, I. M., & Yates, R. B. J. (2019). Singularities of base polynomials and Gau-Wu numbers. *Linear Algebra and its Applications, 581*, 112-127.

Camenga, K. A., Rault, P. X., Sendova, T., & Spitkovsky, I. M. (2014). On the Gau-Wu number for some classes of matrices. *Linear Algebra and Its Applications, 444*, 254-262.

Camenga, K. A., Spitkovsky, I., Rault, P. X., & Yates, R. B. J. (2021). The Gau-Wu Number for 4×4 and Select Arrowhead Matrices. https://arxiv.org/abs/2105.11860.

Cunningham, K. K. A., Edgar, T., Helminck, A. G., Jones, B. F., Oh, H., Schwell, R., & Vasquez, J. F. (2014). On the structure of involutions and symmetric spaces of dihedral groups. *Note di Matematica, 34*(2), 23-40.

Deaett, L., Lafuente-Rodrigues, R. H., Marin Jr., J., Martin, E. H., Patton, L., Rasmussen, K., & Johnson Yates, R. B. (2013). Trace conditions for symmetry of the numerical range. *Electronic Journal of Linear Algebra, 26*, 591-603.

Militzer, E., Patton, L., Spitkovsky, I. M., & Tsai, M.-C. (2017). Numerical ranges of 4-by-4 nilpotent matrices: Flat portions on the boundary. *Operator Theory Advances and Applications, 259*, 561-591.

#### REUF 2009

Fleming, P. S., Garcia, S. R., & Karaali, G. (2011). Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs. *Journal of Number Theory, 131*, 661-680.

#### REUF 2008

Hogben, L. & McLeod, J. (2010). A linear algebraic view of partition regular matrices. *Linear Algebra and its Applications, 433*, 1809-1820.

Hogben, L. & Wilson, U. (2012). Eventual properties of matrices. *Electronic Journal of Linear Algebra, 23*, 953-965.

Hogben, L., Tam, B.-S., & Wilson, U. (2015). Note on the Jordan form of irreducible eventually nonnegative matrix. *Electronic Journal of Linear Algebra, 30*, 279-285.