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