English

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.

Keywords

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

R2 v1 2026-06-23T18:02:15.652Z