# Research Projects

Student Scholarship Recognition Day (SSRD) is held each spring to celebrate the exemplary scholarship and creativity of Willamette University students. Students work directly with faculty members or design and conduct their own research throughout the year.

## Featured Projects

Here are a few projects that exemplify the wonderful research students from the Mathematics department have done over the years.

Abstract: Peg solitaire dates back to the late 17th century, originally played on a board consisting of 33 holes in a grid. Pegs jump over other pegs to remove them, the player winning by ending with a single peg on the board. In 2011, Beeler and Hoilman studied the game on a variety of boards, converting the game into a problem in graph theory. In our research, we allow any number of pegs to be at each hole and jumps to be made on any three adjacent vertices, regardless of their peg counts. Watch out: This means negative pegs! We examine various families of graphs to determine which of them are winnable.

Connor Crowley & Justin Scanlon (2020)

Abstract: In this research we introduce a new graph labeling called a Super Tuple Edge-Magic Total (STEMT) labeling. We map the vertices and edges of a graph to points on the Cartesian plane with a solution, or "magic tuple," found by summing the labels on each edge and its endpoints. Our research investigates which families of graphs have magic tuple solutions and methods of finding those solutions. We investigate families such as paths, cycles, complete graphs, complete bipartite graphs and more.

Gus Mayeno, Gillian Pringle & Lydia Savelli (2020)

Abstract: Graphs can represent the intersections of geometric objects. A particular kind of intersection graph corresponds to bending paths on a grid with overlapping segments. These edge-intersection graphs of paths on a grid (EPG graphs) are generally on square grids. In our research, we have expanded this to consider Euclidean and hyperbolic grids with different polygon faces, and with different numbers of grid lines meeting at each point.

Johannes Griesser & Lucas Perryman-Deskins (2020)

These are all the projects the Mathematics department has presented at SSRD in the last few years.

### 2018

• History of Symmetric Key Ciphers - Jaime McConachie (Thesis)
• Information Theory - Journey Penney (Thesis)
• Index Calculus and Hasse Lifting - Daphne Jacobsen (Thesis)
• Closed Braids and Alexander's Theorem - Alison Najmy (Thesis)
• Region Crossing Change is an Unknotting Operation - Ashlyn Witherwax (Thesis)
• Knot Games: An Investigation on unknotting and smoothing - Jeff Decker (Thesis)
• Separating Examples of the Intersection Graphs of Convex Sub-Polygons of k-Lizards - Kyle Salois
• Creating Problems: The Art of Stamping Graphs - Zechariah Hazel

### 2017

• k-majority Tournaments in Graph Theory - Dane Miyata, Jeremy Coste (Thesis)
• The Accountable Art Gallery Problem - Samuel Coste, Boyuan Lyu (Thesis)
• Efficient Mino Foldings - Taylor Matsumura, Rufei Men, Mattie Wiltbank (Thesis)

### 2015

• Doubly Periodic Functions - Katherine Lacy (Independent Research)
• Intersection Multiplicity for Polynomials - David Livingston (Independent Research)
• Symmetric Key Cryptography - Yang Lin (Independent Research)
• Lattice Based Cryptography - Taylor Mutch (Independent Research)
• Security and Perfect Secrecy - Rebecca Harper (Independent Research)
• Independent Study in Go - Hayden Parker (Independent Research)
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