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Preprint
An Introduction to Algebraic Combinatorics
31 May 2025
Abstract
This is an introduction to algebraic combinatorics, written for a quarter-long graduate course. It starts with a rigorous introduction to formal power series with some combinatorial applications, then discusses integer partitions (proving Jacobi's triple product identity), permutations (Lehmer codes, cycles) and subtractive methods (alternating sums, cancellations and inclusion-exclusion principles, with a particular focus on sign-reversing involutions and determinants). The last chapter introduces symmetric polynomials and proves the Littlewood--Richardson rule using Bender--Knuth involutions (a la Stembridge). The appendix contains over 200 exercises (without solutions).
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Details
- Title
- An Introduction to Algebraic Combinatorics
- Creators
- Darij Grinberg - Drexel University
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022055076204721