Notes on the combinatorial fundamentals of algebra

2020/08/22 by Darij Grinberg, Grinberg, Darij · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.2008.09862

openalex publication_date 2020/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Chio Condensation and Random Sign Matrices
• A combinatorial approach to matrix algebra
• A combinatorial formula for rank 2 cluster variables
• From Chio Pivotal Condensation to the Matrix-Tree theorem
• Determinants of block matrices

Cited by

• The trace Cayley-Hamilton theorem
• On Noether's Degree Bound for Finite Group Schemes
• The pre-Pieri rules

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