Summer of Math Exposition

We should be careful with the terminology. Double counting is used in several ways in both the concept of counting an object twice, as well as two different methodologies to count a set which are different and may cause confusion. I think in introducing the problem, using the example of a graph in a straight line is a simple demonstration and can be added with a simple triangular graph to illustrate why it’s slightly different that we might want to consider additional structure and why it could be useful in this instance.

The text and arguments are also slightly too complex for an undergraduate to read through easily as they would need to very familiar with group theory and would be more suited for a beginner graduate level and this might not click very easily in terms of new connections to a person who is not too familiar with the subject in terms of introducing a new field. In this instance, we may sacrifice some mathematical rigour to try to communicate the ideas of the proof forwards to the reader.

Pretty difficult to read. Feels like one of those handouts by a professor. A student can power through it if needed, but I can’t see those students gaining much interest in the subject.