Combinatorics Math

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. 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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• Top/Science/Math/Algebra/Group Theory
• Top/Science/Math/Probability

• On-line Dictionary of Combinatorics - An expanding web text by Joe Fields.
  
• Enumeration of Polyhedra - Enumeration of polyhedra with up to 9 faces by Steven Dutch.
  
• G-Systems - Theory of chord structures to create music through algorithms by Vladimir Ladma.
  
• 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.
  
• A=B - Downloadable combinatorics text by Marko Petkovsek, Herbert Wilf and Doron Zeilberger. Published by A. K. Peters.
  
• A New Proof of the Four Colour Theorem - By Ashay Dharwadker. Includes profile, research papers for other algorithms, lecture notes, and student database.
  
• The Cutting Sticks Problem - An unsolved combinatorial problem by Frans Faase.
  
• The Combinatorics Net - Maintained by Bill Chen.
  
• Catalogue of Lattices - A catalogue of different types with applications to packing spheres by Neil Sloane and Gabriele Nebe.
  
• Squared Squares - Tilings of squares and rectangles, the classical problem and variations.
  
• Combinatorial Catalogues - Combinatorial objects such as graphs, designs and geometries collected by Gordon Royle.
  
• Combinatorics - MathWorld article with basic definitions and links.
  
• Algebraic Combinatorics via Finite Group Actions - A hypertext by A. Betten, H. Fripertinger and A. Kerber.
  
• The Math Forum Math Library - Combinatorics - Comprehensive catalog of websites relating to Combinatorics.
  
• ArXiv Front: CO Combinatorics - Combinatorics section of the Front for the Mathematics ArXiv.
  
• The Combinatorial Object Server - Select a type together with specific parameter values and COS will return a list of all such combinatorial objects.
  
• CATS: Combinatorial Algorithms Test Sets - Searchable index of problems, links and methodology maintained by the Association for Computing Machinery.
  
• Polya's Enumeration Theorem - An article on generating functions and Polya's theory of counting by Karl Dahlke.
  
• Encyclopedia of Combinatorial Structures - Searchable database of structures with specifications and counts.
  
• Combinatorial Data - Brendan McKay's collection of miscellaneous tables in graph6 or sparse6 format.
  
• Generating Functions - Introduction to generating functions with interactive java applets by Alexander Bogomolny.
  
• Topics in Mathematics - Combinatorics - In the Mathematics Archive at University of Tennessee, Knoxville.
  
• Counting Young Tableaux - An article on counting Young tableaux of bounded height by François Bergeron and Francis Gascon.
  
• Extremal Combinatorics - With Applications in Computer Science by Stasys Jukna.
  
• Enumeration of the Binary Trees - A note on Catalan numbers by Ivan Galkin.
  
• A Survey of Venn Diagrams - Various facts and figures about Venn diagrams by Frank Ruskey.
  
• The Seventeen Wallpaper Groups - Examples in traditional Japanese patterns.
  
  

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