Combinatorics, also called combinatorial mathematics, is the branch of discrete mathematics concerned with enumeration problems,
existence problems, constructions, and structural
properties of discrete objects. Its subjects include graph
theory, permutations, combinations,
and combinatorial designs (West 2020, p. 1).
Enumerative combinatorics is the part concerned specifically with counting finite sets of
objects satisfying prescribed conditions.
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
Explore with Wolfram|Alpha
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.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. https://www.combinatorics.org/ojs/index.php/eljc/issue/archive.Eppstein,
D. "Combinatorial Geometry." https://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." Elec. J. Combin. 2, F1, 1995. https://doi.org/10.37236/1224.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.MathPages.
"Combinatorics." https://www.mathpages.com/home/icombina.htm.Nijenhuis,
A. and Wilf, H. Combinatorial
Algorithms for Computers and Calculators, 2nd ed. New York: Academic Press,
1978.Petit, S. "Encyclopedia of Combinatorial Structures."
https://web.archive.org/web/20170309044045/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." https://web.archive.org/web/20141024161909/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." Elec. J. Combin. 1,
F1, 1994. https://doi.org/10.37236/1194.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.West,
D. B. Combinatorial
Mathematics. Cambridge, England: Cambridge University Press, 2020.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.Referenced
on Wolfram|Alpha
Combinatorics
Cite this as:
Weisstein, Eric W. "Combinatorics." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Combinatorics.html
Subject classifications
