 AMOF: The Amazing Mathematical Object Factory  Frank Ruskey
Combinatorial objects are everywhere. How many ways are there to make change for $1 using unlimited numbers of coins of all denominations? Each way is a combinatorial object. AMOF is part encyclopedia and part calculator, a teaching tool that generates mathematical permutations for such combinatorial objects as subsets and combinations, partitions, magic squares, and Fibonacci sequences by allowing the user to define the parameters of discrete objects. The Object Factory returns a list of all objects that satisfy those parameters. The site can be used to learn more about many types of discrete mathematical structures; descriptions of objects progress in complexity for students at different levels. For more advanced materials, see the Combinatorial Object Server (COS).
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 Combinatorial Object Server (COS)  Frank Ruskey; Dept. of Computer Science, Univ. of Victoria, B.C., Canada
Specify a type of combinatorial object, together with specific parameter values, and COS will return to you a list of 200 such objects. Generation pages: permutations, combinations, various types of trees, unlabelled graphs, linear extensions of posets, pentomino puzzle solutions, numerical partitions, and a host of other objects. This server is designed for researchers and educators; the corresponding version for K12 students and educators runs on Canada's SchoolNet, and is called The Amazing Mathematical Object Factory.
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 Combinatorics  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to combinatorics, loosely the science of counting, studying families of sets (usually finite) with certain characteristic arrangements of their elements or subsets, and asking what combinations are possible, and how many there are. This includes a number of quite elementary topics, such as enumerating all possible permutations or combinations of a finite set. Because of the approachable nature of the subject, combinatorics is often presented with other fields (elementary probability, elementary number theory, and so on) to the exclusion of the more significant aspects of the subject. These include more sophisticated methods of counting sets... History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.
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 Combinatorics (MathPages)  Kevin Brown
About 40 "informal notes" by Kevin Brown on combinatorics: Dedekind's problem, cumulative permutation sequences, the factorial number system, Hardy and Ramanujan on partitions, solving magic squares, collecting k complete sets of coupons, and many more.
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 The Combinatorics Net and Annals Of Combinatorics  Bill Chen
Links to combinatorics articles, groups, conference reports, seminars, journals, books, typesetting and graph drawing, software, preprints, open problems, research announcements, news and stories, and related sites. The Annals of Combinatorics publishes outstanding contributions to combinatorial mathematics in all its aspects.
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