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Summary
The technique of distinguishing one knot from another by coloring arcs and applying some basic modular arithmetic is part of most standard undergraduate knot theory classes. When we study n-colorability, we are usually only interested when n is a prime number. But what if n is composite? What can we say then?
Additional information
Notes on contributors
Sandy Ganzell
Sandy Ganzell ([email protected]) has been teaching math for over 25 years. Originally interested in the topology of 4-manifolds, Sandy has since discovered the joys of knot theory, which has many more open problems that are accessible to students. When not doing math, you can often find Sandy rock climbing, coaching ultimate, or creating crossword puzzles.
Caroline VanBlargan
Caroline VanBlargan ([email protected]) took a knot theory course with Sandy as an undergrad, where she was able to explore fun, open problems in knot theory. Caroline went on to study geometric analysis in graduate school and has been teaching math at Penn State since Fall 2022. Outside of math, Caroline enjoys lifting weights, hiking, and (more recently) playing guitar.