Rahul Sharma (Editor)

Outline of combinatorics

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Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

Contents

Essence of combinatorics

  • Matroid
  • Greedoid
  • Ramsey theory
  • Van der Waerden's theorem
  • Hales–Jewett theorem
  • Umbral calculus, binomial type polynomial sequences
  • Combinatorial species

    • Branches of combinatorics

  • Algebraic combinatorics
  • Analytic combinatorics
  • Arithmetic combinatorics
  • Combinatorics on words
  • Combinatorial design theory
  • Enumerative combinatorics
  • Extremal combinatorics
  • Geometric combinatorics
  • Graph theory
  • Infinitary combinatorics
  • Matroid theory
  • Order theory
  • Partition theory
  • Probabilistic combinatorics
  • Topological combinatorics

    • Multi-disciplinary fields that include combinatorics

  • Coding theory
  • Combinatorial optimization
  • Combinatorics and dynamical systems
  • Combinatorics and physics
  • Discrete geometry
  • Finite geometry
  • Phylogenetics

    • History of combinatorics

    History of combinatorics

    General combinatorial principles and methods

  • Combinatorial principles
  • Trial and error, brute-force search, bogosort, British Museum algorithm
  • Pigeonhole principle
  • Method of distinguished element
  • Mathematical induction
  • Recurrence relation, telescoping series
  • Generating functions as an application of formal power series
  • Cyclic sieving
  • Schrödinger method
  • Exponential generating function
  • Stanley's reciprocity theorem
  • Binomial coefficients and their properties
  • Combinatorial proof
  • Double counting (proof technique)
  • Bijective proof
  • Inclusion–exclusion principle
  • Möbius inversion formula
  • Parity, even and odd permutations
  • Combinatorial Nullstellensatz
  • Incidence algebra
  • Greedy algorithm
  • Divide and conquer algorithm
  • Akra–Bazzi method
  • Dynamic programming
  • Branch and bound
  • Birthday attack, birthday paradox
  • Floyd's cycle-finding algorithm
  • Reduction to linear algebra
  • Sparsity
  • Weight function
  • Minimax algorithm
  • Alpha–beta pruning
  • Probabilistic method
  • Sieve methods
  • Analytic combinatorics
  • Symbolic combinatorics
  • Combinatorial class
  • Exponential formula
  • Twelvefold way
  • MacMahon Master theorem

    • Data structure concepts

  • Data structure
  • Data type
  • Abstract data type
  • Algebraic data type
  • Composite type
  • Array
  • Associative array
  • Deque
  • List
  • Linked list
  • Queue
  • Priority queue
  • Skip list
  • Stack
  • Tree data structure
  • Automatic garbage collection

    • Problem solving as an art

  • Heuristic
  • Inductive reasoning
  • How to Solve It
  • Creative problem solving
  • Morphological analysis (problem-solving)

    • Living with large numbers

  • Names of large numbers, long scale
  • History of large numbers
  • Graham's number
  • Moser's number
  • Skewes' number
  • Large number notations
  • Conway chained arrow notation
  • Hyper4
  • Knuth's up-arrow notation
  • Moser polygon notation
  • Steinhaus polygon notation
  • Large number effects
  • Exponential growth
  • Combinatorial explosion
  • Branching factor
  • Granularity
  • Curse of dimensionality
  • Concentration of measure

    • Persons influential in the field of combinatorics

  • Noga Alon
  • George Andrews
  • József Beck
  • Eric Temple Bell
  • Claude Berge
  • Béla Bollobás
  • Peter Cameron
  • Louis Comtet
  • John Horton Conway
  • On Numbers and Games
  • Winning Ways for your Mathematical Plays
  • Persi Diaconis
  • Ada Dietz
  • Paul Erdős
  • Erdős conjecture
  • Philippe Flajolet
  • Solomon Golomb
  • Ron Graham
  • Ben Green
  • Tim Gowers
  • Jeff Kahn
  • Gyula O. H. Katona
  • Imre Leader
  • László Lovász
  • George Pólya
  • Vojtěch Rödl
  • Gian-Carlo Rota
  • Cecil C. Rousseau
  • H. J. Ryser
  • Dick Schelp
  • Vera T. Sós
  • Joel Spencer
  • Emanuel Sperner
  • Richard P. Stanley
  • Benny Sudakov
  • Endre Szemerédi
  • Terence Tao
  • Carsten Thomassen
  • Jacques Touchard
  • Pál Turán
  • Bartel Leendert van der Waerden
  • Herbert Wilf
  • Richard Wilson
  • Doron Zeilberger

    • Combinatorics scholars

  • Category:Combinatorialists

    • Journals

  • Annals of Combinatorics
  • Ars Combinatoria
  • Australasian Journal of Combinatorics
  • Bulletin of the Institute of Combinatorics and Its Applications
  • Combinatorica
  • Combinatorics, Probability and Computing
  • Computational Complexity
  • Designs, Codes and Cryptography
  • Discrete and Computational Geometry
  • Discrete Applied Mathematics
  • Discrete Mathematics
  • Discrete Mathematics & Theoretical Computer Science
  • Discrete Optimization
  • Discussiones Mathematicae Graph Theory
  • Electronic Journal of Combinatorics
  • European Journal of Combinatorics
  • The Fibonacci Quarterly
  • Finite Fields and Their Applications
  • Geombinatorics
  • Graphs and Combinatorics
  • Integers, Electronic Journal of Combinatorial Number Theory
  • Journal of Algebraic Combinatorics
  • Journal of Automata, Languages and Combinatorics
  • Journal of Combinatorial Designs
  • Journal of Combinatorial Mathematics and Combinatorial Computing
  • Journal of Combinatorial Optimization
  • Journal of Combinatorial Theory, Series A
  • Journal of Combinatorial Theory, Series B
  • Journal of Complexity
  • Journal of Cryptology
  • Journal of Graph Algorithms and Applications
  • Journal of Graph Theory
  • Journal of Integer Sequences (Electronic)
  • Journal of Mathematical Chemistry
  • Online Journal of Analytic Combinatorics
  • Optimization Methods and Software
  • The Ramanujan Journal
  • Séminaire Lotharingien de Combinatoire
  • SIAM Journal on Discrete Mathematics

    • Prizes

  • Euler Medal
  • European Prize in Combinatorics
  • Fulkerson Prize
  • König Prize
  • Pólya Prize

    • References

    Outline of combinatorics Wikipedia
    (Text) CC BY-SA