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Enumerative Combinatorics
This book will bring enjoyment to many future generations of mathematicians and aspiring mathematicians as they are exposed to the beauties and pleasures of enumerative combinatorics. Topics covered includes: What is Enumerative Combinatorics, Sieve Methods, Partially Ordered Sets, Rational Generating Functions, Graph Theory Terminology
Author(s): Richard P. Stanley
725 Pages 
Combinatorics of Centers by Sebastian Konig
This PDF book Combinatorics of Centers of 0-Hecke Algebrasin Type A covers the following topics related to Combinatorics : Introduction, Preliminaries, Coxeter groups, The symmetric group, Combinatorics, enters of 0-Hecke algebras, Elements in stair form, Equivalence classes, etc.
Author(s): Sebastian Konig
59 Pages
Introduction to Combinatorics by UToronto
Combinatotics is about counting without really counting all possible cases one by one. This PDF covers the following topics related to Combinatorics : Introduction, The Pigeonhole Principle, The Principle of Extremals, The Principle of Invariants, Permutations and Combinations, Combinations with Repetition, Inclusion–Exclusion principle, Recurrence Relations, Generating Functions, Partitions of Natural Numbers.
Author(s): Stefanos Aretakis, University of Toronto, Scarborough
63 Pages
Algebraic Combinatorics Lecture Notes
This book explains the following topics: Diagram Algebras and Hopf Algebras, Group Representations, Sn-Representations Intro, Decomposition and Specht Modules, Fundamental Specht Module Properties and Branching Rules, Representation Ring for Sn and its Pieri Formula, Pieri for Schurs, Kostka Numbers, Dual Bases, Cauchy Identity, Finishing Cauchy, Littlewood-Richardson Rule, Frobenius Characteristic Map, Algebras and Coalgebras, Skew Schur Functions and Comultiplication, Sweedler Notation, k-Coalgebra Homomorphisms, Subcoalgebras, Coideals, Bialgebras, Bialgebra Examples, Hopf Algebras Defined, Properties of Antipodes and Takeuchi’s Formula, etc.
Author(s): Sara Billey, Josh Swanson
101 Pages
This lecture note covers the following topics: What is Combinatorics, Permutations and Combinations, Inclusion-Exclusion-Principle and Mobius Inversion, Generating Functions, Partitions, Partially Ordered Sets and Designs.
Author(s): Torsten Ueckerdt
137 Pages
The purpose of this note is to give students a broad exposure to combinatorial mathematics, using applications to emphasize fundamental concepts and techniques. Topics covered includes: Introduction to Combinatorics, Strings, Sets, and Binomial Coefficients, Induction, Combinatorial Basics, Graph Theory, Partially Ordered Sets, Generating Functions, Recurrence Equations , Probability, Applying Probability to Combinatorics, Combinatorial Applications of Network Flows, Polya’s Enumeration Theorem.
Author(s): Mitchel T. Keller and William T. Trotter
346 Pages
This book covers the following topics: Fibonacci Numbers From a Cominatorial Perspective, Functions,Sequences,Words,and Distributions, Subsets with Prescribed Cardinality, Sequences of Two Sorts of Things with Prescribed Frequency, Sequences of Integers with Prescribed Sum, Combinatorics and Probability, Binary Relations, Factorial Polynomials, The Calculus of Finite Differences, Principle of Inclusion and Exclusions.
Author(s): Carl G. Wagner
120 Pages
ANALYTIC COMBINATORICS SYMBOLIC COMBINATORICS
Author(s): Philippe Flajolet and Robert Sedgewick
196 Pages
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An Architecture for Combinator Graph Reduction
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Foundations of Combinatorics with Applications
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