Samples from an upcoming project
I am currently writing an algebra textbook that is as comprehensive as I can make it. It is perhaps never going to be refined into something publishable, but is mainly meant as a resource for myself in my own voice. Maybe some part of it will be worthwhile to you. These sections are still VERY under construction and should be treated as such. Typos or more hazardous errors will occur. Also, the internal reference links were handled lazily and will mostly be broken.
Clique Polynomials Project
A project I picked up in high school as a mere child. It helped me grow into a fair bit of my mathematical maturity under supervision of combinatorialist and representation theorist Dr. Aparna Upadhyay over several semesters of undergrad. Here is a summary of my progress. I am currently in the process of reteaching myself so as to resume work. From our work in the study of what we called substacks of Hamming cliques, it is clear in our hearts that the method which got us our first and only nontrivial term can be pushed through a clever partial order on compositions and stacks into a generating function.