Notes on the combinatorial fundamentals of algebra
Abstract
This is a detailed survey  with rigorous and selfcontained 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 arXiv:
 arXiv:2008.09862
 Bibcode:
 2020arXiv200809862G
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 1403 pages. v3 corrects typos and adds Exercises 6.656.69. Not a textbook