Notes on the combinatorial fundamentals of algebra
Combinatorics
2022-09-16 v3
Abstract
This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is entirely expository (and written to a large extent as a repository for folklore proofs); no new results (and few, if any, new proofs) appear.
Cite
@article{arxiv.2008.09862,
title = {Notes on the combinatorial fundamentals of algebra},
author = {Darij Grinberg},
journal= {arXiv preprint arXiv:2008.09862},
year = {2022}
}
Comments
1403 pages. v3 corrects typos and adds Exercises 6.65--6.69. Not a textbook; rather a repository of proofs I could cite. Posted here for easier referencing (and long-term archival). This project is tracked on https://github.com/darijgr/detnotes