Combinatorics (original) (raw)

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Combinatorics is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their properties.

Mathematicians sometimes use the term "combinatorics" to refer to a larger subset of discrete mathematics that includesgraph theory. In that case, what is commonly called combinatorics is then referred to as "enumeration."

The Season 1 episode "Noisy Edge" (2005) of the television crime drama NUMB3RS mentions combinatorics.

See also

Algebraic Combinatorics, Antichain, Chain, Concrete Mathematics, Dilworth's Lemma, Dirichlet's Box Principle, Discrete Mathematics,Enumeration Problem, Erdős-Szekeres Theorem, Inclusion-Exclusion Principle,Kirkman's Schoolgirl Problem, Kirkman Triple System, Partial Order, Partial Order Length, Partial Order Width, Ramsey's Theorem, Schröder-Bernstein Theorem,Schur's Lemma, Sperner's Theorem, Total Order, Umbral Calculus, van der Waerden's Theorem Explore this topic in the MathWorld classroom

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References

Abramowitz, M. and Stegun, I. A. (Eds.). "Combinatorial Analysis." Ch. 24 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 821-827, 1972.Aigner, M. Combinatorial Theory. New York: Springer-Verlag, 1997.Balakrishnan, V. K.Schaum's Outline of Combinatorics, including Concepts of Graph Theory. New York: McGraw-Hill, 1995.Bellman, R. and Hall, M. Combinatorial Analysis. Amer. Math. Soc., 1979.Berge, C. Principles of Combinatorics. New York: Academic Press, 1971.Bergeron, F.; Labelle, G.; and Leroux, P. Combinatorial Species and Tree-Like Structures. Cambridge, England: Cambridge University Press, 1998.Biggs, N. L. "The Roots of Combinatorics."Historia Mathematica 6, 109-136, 1979.Bose, R. C. and Manvel, B. Introduction to Combinatorial Theory. New York: Wiley, 1984.Cameron, P. J.Combinatorics: Topics, Techniques, Algorithms. New York: Cambridge University Press, 1994.Cohen, D. Basic Techniques of Combinatorial Theory. New York: Wiley, 1978.Cohen, D. E. Combinatorial Group Theory: A Topological Approach. New York: Cambridge University Press, 1989.Colbourn, C. J. and Dinitz, J. H. (Eds.). CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, 1996.MathPages. "Combinatorics." http://www.mathpages.com/home/icombina.htm.Comtet, L. Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, 1974.Coolsaet, K. "Index of Combinatorial Objects." http://gonzo.hogent.be/~kc/ico/Dinitz, J. H. and Stinson, D. R. (Eds.). Contemporary Design Theory: A Collection of Surveys. New York: Wiley, 1992.Eisen, M. Elementary Combinatorial Analysis. New York: Gordon and Breach, 1969.Electronic Journal of Combinatorics. http://www.combinatorics.org/previous_volumes.html.Eppstein, D. "Combinatorial Geometry." http://www.ics.uci.edu/~eppstein/junkyard/combinatorial.html.Erdős, P. and Spencer, J. Probabilistic Methods in Combinatorics. New York: Academic Press, 1974.Erickson, M. J. Introduction to Combinatorics. New York: Wiley, 1996.Fields, J. "On-Line Dictionary of Combinatorics." http://www.math.uic.edu/~fields/comb_dic/.Gardner, M. "Combinatorial Theory." Ch. 3 in The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University of Chicago Press, pp. 19-28, 1984.Godsil, C. D. "Problems in Algebraic Combinatorics." Electronic J. Combinatorics 2, No. 1, R1, 1-20, 1995. http://www.combinatorics.org/Volume_2/Abstracts/v2i1r1.html.Graham, R. L.; Grötschel, M.; and Lovász, L. (Eds.). Handbook of Combinatorics, 2 vols. Cambridge, MA: MIT Press, 1996.Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, 1994.Grimaldi, R. P. Discrete and Combinatorial Mathematics: An Applied Introduction, 4th ed. Longman, 1998.Hall, M. Jr. Combinatorial Theory, 2nd ed. New York: Wiley, 1986.Harary, F. Applied Combinatorial Mathematics. New York: Wiley, 1964.Knuth, D. E. (Ed.). Stable Marriage and Its Relation to Other Combinatorial Problems. Providence, RI: Amer. Math. Soc., 1997.Kreher, D. L. and Stinson, D. Combinatorial Algorithms: Generation, Enumeration, and Search. Boca Raton, FL: CRC Press, 1999.Kučera, L. Combinatorial Algorithms. Bristol, England: Adam Hilger, 1989.Liu, C. L.Introduction to Combinatorial Mathematics. New York: McGraw-Hill, 1968.MacMahon, P. A. Combinatory Analysis, 2 vols. New York: Chelsea, 1960.Marcus, D. Combinatorics: A Problem Oriented Approach. Washington, DC: Math. Assoc. Amer., 1998.Nijenhuis, A. and Wilf, H. Combinatorial Algorithms for Computers and Calculators, 2nd ed. New York: Academic Press, 1978.Petit, S. "Encyclopedia of Combinatorial Structures."http://algo.inria.fr/encyclopedia/.Raghavarao, D. Constructions and Combinatorial Problems in Design of Experiments. New York: Dover, 1988.Riordan, J. Combinatorial Identities, reprint ed. with corrections. Huntington, NY: Krieger, 1979.Riordan, J. An Introduction to Combinatorial Analysis. New York: Wiley, 1980.Roberts, F. S. Applied Combinatorics. Englewood Cliffs, NJ: Prentice-Hall, 1984.Rosen, K. H. (Ed.). Handbook of Discrete and Combinatorial Mathematics. Boca Raton, FL: CRC Press, 2000.Rota, G.-C. (Ed.). Studies in Combinatorics. Providence, RI: Math. Assoc. Amer., 1978.Ruskey, F. "The (Combinatorial) Object Server." http://www.theory.csc.uvic.ca/~cos/.Ryser, H. J. Combinatorial Mathematics. Buffalo, NY: Math. Assoc. Amer., 1963.Skiena, S.Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.Sloane, N. J. A. "An On-Line Version of the Encyclopedia of Integer Sequences." http://www.research.att.com/~njas/sequences/eisonline.html.Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press, 1995.Slomson, A. Introduction to Combinatorics. Boca Raton, FL: Chapman and Hall, 1997.Stanley, R. P. Enumerative Combinatorics, Vol. 1. Cambridge, England: Cambridge University Press, 1999.Stanley, R. P. Enumerative Combinatorics, Vol. 2. Cambridge, England: Cambridge University Press, 1999.Street, A. P. and Wallis, W. D. Combinatorial Theory: An Introduction. Winnipeg, Manitoba: Charles Babbage Research Center, 1977.Tucker, A. Applied Combinatorics, 3rd ed. New York: Wiley, 1995.van Lint, J. H. and Wilson, R. M. A Course in Combinatorics. New York: Cambridge University Press, 1992.Weisstein, E. W. "Books about Combinatorics." http://www.ericweisstein.com/encyclopedias/books/Combinatorics.html.Wilf, H. S. Combinatorial Algorithms: An Update. Philadelphia, PA: SIAM, 1989.

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Combinatorics

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Weisstein, Eric W. "Combinatorics." FromMathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Combinatorics.html

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