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	Combinatorics - Wikipedia, the free encyclopedia
		Muslim mathematicians later studied combinatorial analysis from at least the 13th century.
		Ibn Mun'im, in the Maghreb of North Africa in the early 13th century, dealt with combinatory problems.
		There are many combinatorial patterns and theorems related to the structure of combinatoric sets.
	en.wikipedia.org /wiki/Combinatorics (2346 words)

	Combinatorial proof - Wikipedia, the free encyclopedia
		A combinatorial proof is a method of proving a statement, usually a combinatorics identity, by counting some carefully chosen object in different ways to obtain different expressions in the statement (see also double counting).
		A statement is said to be proven combinatorially if a combinatorial argument, or counting argument, is used in the aforementioned fashion to justify the key steps of its proof.
		This technique is particularly useful in areas of discrete mathematics such as combinatorics, graph theory, and number theory.
	en.wikipedia.org /wiki/Combinatorial_proof (407 words)

	Combinatorial Chemistry
		Combinatorial chemistry's potential for accelerating drug discovery-its primary focus so far-has proven to be so compelling that few if any pharmaceutical companies have been able to ignore it, even if they may have wanted to.
		Combinatorial chemistry has been referred to in various ways, such as "molecular evolution," "in vitro selection," and" molecular diversity." But Persidis said he believes there is a need for a term that is more encompassing.
		Combinatorial efforts to hit G-protein receptor targets also are being pursued at Synaptic Pharmaceutical, Paramus, N.J. Stewart A. Noble, vice president of chemistry, described small-molecule libraries constructed as sources of new or improved drugs for G-protein receptor-related disorders and also as probes of receptor function.
	pubs.acs.org /hotartcl/cenear/980406/comb.html (7598 words)

	The Combinatorial Design Approach to Automatic Test Generation
		Combinatorial designs [1] are mathematical constructions widely used in medical and industrial research to construct efficient statistical experiments.
		The combinatorial design tests uncovered faults in the code and in the requirements that were not detected by the standard test process.
		A related approach [11, 12, 13] is the use of orthogonal arrays, a pairwise combinatorial design with the additional property of requiring every pair of values to occur exactly the same number of times.
	www.argreenhouse.com /papers/gcp/AETGissre96.shtml (3238 words)

	C&EN 970224 - Combinatorial Chemistry
		Combinatorial chemistry--a set of techniques for creating a multiplicity of compounds and then testing them for activity--has been widely adopted by large and small drug discovery companies alike over the past few years.
		The idea of combinatorial chemistry is to form large "libraries" of molecules en masse--instead of synthesizing compounds one by one, as has been done traditionally--and to identify the most promising "lead" pharmaceutical compounds by high-throughput screening of the libraries.
		In combinatorial chemistry, as in opera, it isn't over until the fat lady sings--meaning usually that a lead compound is in the drug development pipeline.
	pubs.acs.org /hotartcl/cenear/970224/comb.html (4457 words)

	Combinatorial synthesis discoveries (Site not responding. Last check: 2007-11-06)
		Combinatorial synthesis enables materials scientists to create thousands of complex materials in the time it normally takes to create one.
		The MR compounds in the study are members of a materials class known as perovskite oxides, conductive metal crystals that are made of complex ratios of four to six metal atoms.
		In the past, combinatorial approaches have been used successfully by researchers in the life sciences, who have searched for potential drugs by screening vast libraries of protein combinations.
	www.lbl.gov /Science-Articles/Archive/magnetoresistive.html (607 words)

	CBMS Conference Probabilistic and Combinatorial Approach in Analysis
		We show how the combinatorial results of the previous lecture can be used to estimate the Banach-Mazur distance from a given convex body to a cube of the same dimension.
		We discuss the relation between the combinatorial dimension of a set and the probabilistic properties of a random process indexed by this set.
		We use random coordinate projections to show that the size of the combinatorial structure constructed in the previous lecture is independent of the dimension of the convex body.
	www.math.kent.edu /math/CBMS.cfm (449 words)

	Combinatorial Pyramids
		Combinatorial Pyramids is a tool to study the triangle and its brothers in a three-dimension, computer-animated world.
		Combinatorial Pyramids was inspired by an earlier project by Lynne Kelly, principal of the Virtual School for the Gifted.
		Combinatorial Pyramids is an application written in C using the OpenGL and GLUT libraries.
	archive.ncsa.uiuc.edu /Classes/MATH198/bholt/comb.html (1451 words)

	Multiobjective optimization of combinatorial libraries
		While some of the underlying principles have their origin in the field of statistical experimental design, the first reports dealing specifically with combinatorial libraries were presented in 1995 by five independent groups [4–8].
		Unlike traditional combinatorial approaches, in which the entire library is made and tested in a single conceptual step, DirectedDiversity physically synthesizes, characterizes and tests only a portion of that library at a time.
		A common goal in combinatorial library design is to produce arrays of compounds that are predicted to be highly active against a predefined target according to some quantitative structure-activity or receptor binding model.
	www.research.ibm.com /journal/rd/453/agrafiotis.html (9271 words)

	Amazon.com: Combinatorial Chemistry: Synthesis and Application: Books: Stephen R. Wilson,Anthony W. Czarnik (Site not responding. Last check: 2007-11-06)
		Combinatorial chemistry, a method for synthesizing millions of chemical compounds much faster than usual, is becoming one of the most useful technical tools available to chemists and researchers working today.
		Combinatorial Chemistry: Synthesis and Application details critical aspects of the technique, featuring the work of some of the world's leading chemists, many of whom played a key role in its development.
		Combinatorial Chemistry introduces organic, medicinal, and pharmaceutical chemists as well as biochemists to this exciting, cost-effective, and practical technique, which has unlocked creative potential for the next millennium.
	www.amazon.com /exec/obidos/tg/detail/-/047112687X?v=glance (1019 words)

	Combinatorial Chemistry Notes (Site not responding. Last check: 2007-11-06)
		Combinatorial chemistry (or CombiChem) is an innovative method of synthesizing many different substances quickly and at the same time.
		Combinatorial chemistry contrasts with the time-consuming and labor intensive methods of traditional chemistry where compounds are synthesized individually, one at a time.
		While combinatorial chemistry is primarily used by organic chemists who are seeking new drugs, chemists are also now applying combinatorial chemistry to other fields such as semiconductors, superconductors, catalysts and polymers.
	www.screening-compounds.com (200 words)

	Combinatorial Chemistry: A Guide for Librarians
		Combinatorial chemistry has grown to such an extent that there are now departments, and research groups that incorporate the terms "combinatorial" or "high throughput" as part of their corporate name.
		Combinatorial is an established term in mathematics where it defines the analysis of various kinds of mathematical combinations.
		Combinatorial chemistry is a new field of chemistry that employs novel concepts and techniques to rapidly synthesize and screen large numbers of compounds.
	www.istl.org /02-winter/refereed.html (4574 words)

	Encyclopedia of Combinatorial Structures (Introduction) (Site not responding. Last check: 2007-11-06)
		Sloane's Encyclopedia of Integer Sequences with an emphasis on sequences that arise in the context of decomposable combinatorial structures.
		The restriction to sequences arising in this combinatorial framework has for advantage that in many cases a lot of information can be computed automatically.
		A sequence of integers: the (n+1)th term of this sequence is the number of objects of size n defined by the specification.
	pauillac.inria.fr /algo/encyclopedia/intro.html (366 words)

	combinatorial scientific computing
		"Combinatorial scientific computing," a recently coined label for interdisciplinary research involving discrete mathematics in scientific computing, refers to the development, analysis, and application of combinatorial algorithms to solve problems in computational science and engineering.
		Several of the combinatorial themes discussed at the workshop have taken center stage in CSC research during the past twenty years.
		Combinatorial problems akin to vertex elimination in sparse matrix factorization also arise in automatic differentiation.
	www.siam.org /siamnews/12-04/CSC.htm (1572 words)

	Wiley::Combinatorial Strategies in Biology and Chemistry
		Because combinatorial chemistry evolved from the requirements of the biology field, the authors have written this book with both biologists and chemists in mind.
		Combinatorial chemistry is a new and highly influential area of modern synthetic chemistry based on efficient, parallel synthesis of molecules, as opposed to the use of several synthetic steps, to produce many sets of compounds for biological evaluation.
		Combinatorial Methods in Chemistry and Biology describes the origins, basics and techniques used both in combinatorial chemistry and molecular biology.
	eu.wiley.com /WileyCDA/WileyTitle/productCd-0471497266.html (448 words)

	SIAM Workshop on Combinatorial Scientific Computing
		Combinatorial algorithms and mathematics are a critical enabling technology for scientific computing, especially for large-scale problems and high-performance computers.
		Researchers developing and applying combinatorial mathematics and algorithms in different areas of scientific computing have a great deal of overlap in their interests, mathematical aesthetics, objectives, and tools.
		As a consequence, combinatorial algorithms researchers in these sub-communities tend to be isolated and unaware of the broader sets of problems, techniques, and researchers.
	www.siam.org /meetings/pp04/cscworkshop.htm (471 words)

	Combinatorial Auctions
		Combinatorial auctions are the great frontier of auction theory today, and this book provides a state-of-the-art survey of this exciting field.
		Combinatorial Auctions is an important interdisciplinary field combining issues from economics, game theory, optimization, and computer science.
		Combinatorial Auctions is a major advance in the theory and practice of market design.
	www.cramton.umd.edu /papers2000-2004/combinatorial-auctions-book-public.htm (526 words)

	Combinatorial Optimization - TU/e (Site not responding. Last check: 2007-11-06)
		The Combinatorial Optimization Group focuses on problems of the form: determine a solution which, given a number of boundary conditions, minimizes the costs, or maximizes the proceeds.
		Combinatorial Optimization goes into problems in operational management, such as the distribution and production planning, and more technical problems, which for example occur with the design and operating of computer systems.
		Combinatorial optimization is an interesting worker's field for the applied operational researcher, who's profession it is to handle such practical situations.
	www.win.tue.nl /math/bs/comb_opt (189 words)

	What is Combinatorial Chemistry?
		The active ingredients are actually mixtures of 100 or more deadly venoms, essentially produced by the combinatorial scrambling of amino acids.
		And it is with amino acids that modern combinatorial chemistry began.
		These will be the fascinating questions that those involved in combinatorials will be wrestling with in the years to come.
	www.imd3.org /combichem.html (744 words)

	Combinatorial Software
		The (Combinatorial) Object Server: maintained by Frank Ruskey, is an on-line device, which, on specifying a type of combinatorial object, together with specific parameter values, will return to you a list of all such objects.
		It is intended to be the young cousin of Sloane's Encyclopedia of Integer Sequences with an emphasis on sequences that arise in the context of decomposable combinatorial structures.
		Groups and Graphs: is a software package for graphs, digraphs, geometric configurations, combinatorial designs, and their automorphism groups.
	www.mat.univie.ac.at /~slc/divers/software.html (2130 words)

	Combinatorial Dynamics by Michal Misiurewicz
		Note: Detailed treatment of Combinatorial Dynamics in dimension 1 (with an extensive bibliography and historical remarks) can be found in the book [1].
		Combinatorial Dynamics deals with types of cycles (defined in various ways and not only for interval maps), their coexistence, complexity (usually measured by the topological entropy of the system) and properties of maps with cycles of a given type.
		The word "Combinatorial" refers not only to the fact that we often deal with permutations, but also to the techniques involved in the proofs, that are often of a combinatorial nature.
	at.yorku.ca /t/a/i/c/41.htm (1425 words)

	Combinatorial Website - New Articles
		Combinatorial Synthesis of Heterocycles: Solid Phase Synthesis of 2-Arylquinoline-4-carboxylic Acid Derivatives Gopalsamy, A.; Pallai, P. Tetrahedron Lett.
		Combinatorial Approaches to Pharmacophoric Heterocycles: A Solid-Phase Synthesis of 3,1-Benzoxazine-4-Ones Gordeev, M. Biotechnology and Bioengineering (Combinatorial Chemistry) 1998, 61, 1, 13-16.
		Combinatorial Modification of 2-Ketopiperazine with Solid Phase C-Alkylation and N-Acylations Zhu, Z.; Mckittrick, B. Tetrahedron Lett.
	www.combinatorial.com /new.html (10065 words)

	Wiley::Combinatorial Geometry
		A complete, self-contained introduction to a powerful and resurging mathematical discipline … Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes Tóth, Rogers, and Erd???s.
		Combinatorial Geometry will be of particular interest to mathematicians, computer scientists, physicists, and materials scientists interested in computational geometry, robotics, scene analysis, and computer-aided design.
		It is also a superb textbook, complete with end-of-chapter problems and hints to their solutions that help students clarify their understanding and test their mastery of the material.
	www.wiley.com /WileyCDA/WileyTitle/productCd-0471588903.html (149 words)

	Combinatorial Expression (Site not responding. Last check: 2007-11-06)
		In combinatorics the term mainly used is nCr which literally means the number of ways r things can be taken from n things.
		A combinatorial expression may involve many such terms with arithmatic operators.
		In this problem you have to evaluate a combinatorial expression involving only multiplication and division of nCr.
	acm.uva.es /p/v103/10329.html (207 words)

	TCS - Studies - T-79.250 Combinatorial Models and Stochastic Algorithms
		Stochastic methods such as MCMC sampling, simulated annealing and genetic algorithms are currently at the forefront of approximate techniques for dealing with computationally demanding problems.
		Combinatorial models: elements of statistical mechanics; the Ising model, spin glasses, neural networks.
		The problems are likely to be largely the same as in Spring 2003; however the ordering will be different.
	www.tcs.hut.fi /Studies/T-79.250 (858 words)

	Combinatorial Games (Erik Demaine)
		In general, combinatorial game theory is a suite of techniques for analyzing such games.
		Two versions of ``Playing Games with Algorithms: Algorithmic Combinatorial Game Theory'' are available: the full draft (recommended), and a shorter version appearing in the 26th Symposium on Mathematical Foundations in Computer Science.
		We analyze the complexity of deciding "mate in 1", which is a combinatorial puzzle.
	theory.lcs.mit.edu /~edemaine/games (840 words)

	Wiley::Combinatorial Chemistry and Molecular Diversity in Drug Discovery
		Through the rapidly evolving technology of combinatorial chemistry, it is now possible to produce libraries of small molecules to screen for novel bioactivities.
		The authors, industrial and academic experts in the field, apply combinatorial technologies to drug discovery and development and place co-evolving technologies and practices in a global framework.
		Combinatorial Chemistry and Molecular Diversity in Drug Discovery is one of the first comprehensive books to cover this explosive area.
	eu.wiley.com /WileyCDA/WileyTitle/productCd-0471155187.html (411 words)

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