I’m very excited about undergraduate research! Undergraduate research is what originally made me want to go to graduate school and become a mathematician. **If you are a UT Tyler student interested in doing undergraduate research, email me at karcher@uttyler.edu.**

You can read here about my work the the **UT Tyler REU** and research done with the **graduate Algebra students and undergraduate Algebra II **students.

### REU at UT TYLER

I mentored an REU group during Summer 2017 comprised of three students: Adam Gregory, Bryan Pennington, and Stephanie Slayden.

We defined a variation of Stirling permutations by extending a bijection from increasing labeled ordered trees to Stirling permutations to be defined instead on all labeled ordered trees. We obtained permutations of the set {1,1,2,2,…,n,n} that avoid the patterns 1212 and 2121. We studied pattern avoidance and some statistics of these permutations. Our paper, entitled `Pattern-restricted quasi-Stirling permutations’ is available on arXiv at arXiv:1804.07267 and is currently under review.

### RESEARCH in the ALGEBRA CLASSROOM

During Fall 2017, I worked with another faculty member to facilitate research in groups of graduate and undergraduate students. I was teaching graduate Algebra and my colleague, Lindsey-Kay Lauderdale, was teaching undergraduate Algebra II. We created groups with 2 graduate students and 3 undergraduate students and presented them with a open problem to think about. One was in group theory, two in algebraic graph theory, one in enumerative combinatorics and representation theory, and one on arithmetical structures. We have one conference paper accepted, two papers submitted, and one more paper in preparation from the research completed by these groups.

### STUDENT CONFERENCES in TEXAS

There are are a couple local conferences that we encourage students to attend. In the fall, we typically travel with students to the Texas Undergraduate Mathematics Conference (TUMC), and in the spring we travel to the MAA Texas Section meeting. If you are a student who has done research at UT Tyler, please consider giving a talk at one of these conferences. If you are interested or think you may be interested in math research, send me an email and I can give you the details for the next conference.