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Combinatorics :
Combinatorics studies problems involving finite sets of objects that are defined by certain specified properties. For example, the objects in question may themselves be sets, numbers, graphs or other geometrical configurations. Enumerative combinatorics is concerned with counting the number of objects of a certain kind. Extremal combinatorics is concerned with finding the optimal objects of a certain kind. Topological methods, algebraic methods and even probabilistic methods have been used to solve combinatorial problems. Computer algorithms have also been used to solve some seemingly intractable combinatorial problems. Conversely, combinatorial methods have been used successfully to solve problems in many areas of mathematics and computer science. Here is a sample problem that would use combinatorics: Strangers and Acquaintances (F.P. Ramsey 1930): What is the least number of people that you need to have in a room so that there is always a group of three mutual strangers or a group of three mutual acquaintances? The answer is six.
Associated Categories for Combinatorics
Open Problems
Software
Combinatorial Game Theory
People
Design Theory
Journals
Graph Theory
Events
Research Groups
27 web sites matced for Combinatorics
East Side, West Side
Lecture notes by Herbert S. Wilf on generating combinatorial objects and Maple.

The Combinatorics Net
Maintained by Bill Chen.

ArXiv Front: CO Combinatorics
Combinatorics section of the Front for the Mathematics ArXiv.

Enumeration of the Binary Trees
A note on Catalan numbers by Ivan Galkin.

The Combinatorial Object Server
Select a type together with specific parameter values and COS will return a list of all such combinatorial objects.

Topics in Mathematics - Combinatorics
In the Mathematics Archive at UTK.

Extremal Combinatorics
With Applications in Computer Science by Stasys Jukna.

Encyclopedia of Combinatorial Structures
Searchable database of structures with specifications and counts.

Algebraic Combinatorics via Finite Group Actions
A hypertext by A. Betten, H. Fripertinger and A. Kerber.

CATS: Combinatorial Algorithms Test Sets
Searchable index of problems, links and methodology maintained by the Association for Computing Machinery.

A Survey of Venn Diagrams
Various facts and figures about Venn diagrams by Frank Ruskey.

G-Systems
Theory of chord structures to create music through algorithms by Vladimir Ladma.

Combinatorics
Subfields in the AMS MSC 2000 classification 05.

Combinatorial Data
Brendan McKay's collection of miscellaneous tables in graph6 or sparse6 format.

Catalogue of Lattices
A catalogue of different types with applications to packing spheres by Neil Sloane and Gabriele Nebe.

The Math Forum Math Library - Combinatorics
Comprehensive catalog of websites relating to Combinatorics.

Generating Functions
Introduction to generating functions with interactive java applets by Alexander Bogomolny.

Operational Research Programming Trivia
Computer code for research algorithms in operational research and combinatorial optimization.

Combinatorial Catalogues
Combinatorial objects such as graphs, designs and geometries collected by Gordon Royle.

On-line Dictionary of Combinatorics
An expanding web text by Joe Fields.

Series Expansions
Iwan Jensen counts polyominoes (aka lattice animals), paths, and various related quantities.

Lectures in Combinatorics
An introduction to partially ordered sets, Dilworth's theorem, lattices and combinatorial geometries.

The Cutting Sticks Problem
An unsolved combinatorial problem by Frans Faase.

Combinatorics
MathWorld article with basic definitions and links.

Algebraic Combinatorics via Finite Group Actions
HTML book by A. Betten, H. Fripertinger, and A. Kerber.

A Catalogue of Lattices
By Gabriele Nebe and Neil Sloane.

CATS: Combinatorial Algorithms Test Sets
Searchable index of problems, links and methodology.

 
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