Undergraduate Research

Michael P. Knapp

On this page, I will list some research projects I am interested in that would be suitable for undergraduate students, and give brief descriptions. You can click on the titles for more complete descriptions. This page is small now, but it will grow as I find more projects which interest me.

Generating Weakly Complete Sequences
I have a rule which I use to make sequences of positive integers with the following property: there is some number N such that every integer larger than N can be written as a sum of terms in the sequence. If you use this rule to generate sequences, then the sequences you get seem to have some very nice patterns. The point of this project would be to try to prove that these patterns always exist.

Chromatic Polynomials with Restrictions
Chromatic polynomials are a fundamental concept in graph theory. If you have a graph, then the chromatic polynomial tells you how many ways there are to color the vertices of the graph so that vertices connected by an edge have different colors (I'll define what these terms mean if you click the link). I think that it would be interesting to study this problem if you limit the number of times each color can be used.