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.
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Downloadable combinatorics text by Marko Petkovsek, Herbert Wilf and Doron Zeilberger. Published by A. K. Peters.
Algebraic Combinatorics via Finite Group Actions
A hypertext by A. Betten, H. Fripertinger and A. Kerber.
ArXiv Front: CO Combinatorics
Combinatorics section of the Front for the Mathematics ArXiv.
Brendan McKay's collection of miscellaneous tables in graph6 or sparse6 format.
MathWorld article with basic definitions and links.
The Combinatorics Net
Maintained by Bill Chen.
The Cutting Sticks Problem
An unsolved combinatorial problem by Frans Faase.
Encyclopedia of Combinatorial Structures
Searchable database of structures with specifications and counts.
Enumeration of Polyhedra
Enumeration of polyhedra with up to 9 faces by Steven Dutch.
Enumeration of the Binary Trees
A note on Catalan numbers by Ivan Galkin.
With Applications in Computer Science by Stasys Jukna.
Theory of chord structures to create music through algorithms by Vladimir Ladma.
Introduction to generating functions with interactive java applets by Alexander Bogomolny.
The Math Forum Math Library - Combinatorics
Comprehensive catalog of websites relating to Combinatorics.
Polya's Enumeration Theorem
An article on generating functions and Polya's theory of counting by Karl Dahlke.
Iwan Jensen counts polyominoes (aka lattice animals), paths, and various related quantities.
Tilings of squares and rectangles, the classical problem and variations.
Topics in Mathematics - Combinatorics
In the Mathematics Archive at University of Tennessee, Knoxville.
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Last update:September 23, 2016 at 9:45:08 UTC