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 includes
graph 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
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
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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. Aigner, M. Combinatorial
Theory. Balakrishnan, V. K.
Schaum's
Outline of Combinatorics, including Concepts of Graph Theory. Bellman, R. and Hall, M. Combinatorial
Analysis. Berge, C. Principles
of Combinatorics. Bergeron, F.;
Labelle, G.; and Leroux, P. Combinatorial
Species and Tree-Like Structures. Biggs, N. L. "The Roots of Combinatorics."
Historia Mathematica 6 , 109-136, 1979. Bose, R. C.
and Manvel, B. Introduction
to Combinatorial Theory. Cameron, P. J.
Combinatorics:
Topics, Techniques, Algorithms. Cohen,
D. Basic
Techniques of Combinatorial Theory. Cohen,
D. E. Combinatorial
Group Theory: A Topological Approach. Colbourn, C. J. and Dinitz, J. H. (Eds.). CRC
Handbook of Combinatorial Designs. MathPages.
"Combinatorics." http://www.mathpages.com/home/icombina.htm . Comtet,
L. Advanced
Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. http://gonzo.hogent.be/~kc/ico/ Dinitz,
J. H. and Stinson, D. R. (Eds.). Contemporary
Design Theory: A Collection of Surveys. Eisen,
M. Elementary
Combinatorial Analysis. 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. Erickson,
M. J. Introduction
to Combinatorics. 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. 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. Graham,
R. L.; Knuth, D. E.; and Patashnik, O. Concrete
Mathematics: A Foundation for Computer Science, 2nd ed. Grimaldi, R. P. Discrete
and Combinatorial Mathematics: An Applied Introduction, 4th ed. Hall, M. Jr. Combinatorial
Theory, 2nd ed. Harary, F. Applied
Combinatorial Mathematics. New York: Wiley, 1964. Knuth, D. E.
(Ed.). Stable
Marriage and Its Relation to Other Combinatorial Problems. Kreher, D. L. and Stinson, D. Combinatorial
Algorithms: Generation, Enumeration, and Search. Kučera, L. Combinatorial
Algorithms. Liu, C. L.
Introduction
to Combinatorial Mathematics. MacMahon,
P. A. Combinatory
Analysis, 2 vols. Marcus, D. Combinatorics:
A Problem Oriented Approach. Nijenhuis,
A. and Wilf, H. Combinatorial
Algorithms for Computers and Calculators, 2nd ed. Petit, S. "Encyclopedia of Combinatorial Structures."
http://algo.inria.fr/encyclopedia/ . Raghavarao,
D. Constructions
and Combinatorial Problems in Design of Experiments. Riordan,
J. Combinatorial
Identities, reprint ed. with corrections. Riordan,
J. An
Introduction to Combinatorial Analysis. Roberts,
F. S. Applied
Combinatorics. Rosen,
K. H. (Ed.). Handbook
of Discrete and Combinatorial Mathematics. Rota,
G.-C. (Ed.). Studies
in Combinatorics. Ruskey,
F. "The (Combinatorial) Object Server." http://www.theory.csc.uvic.ca/~cos/ . Ryser,
H. J. Combinatorial
Mathematics. Skiena, S.
Implementing
Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. 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. Slomson,
A. Introduction
to Combinatorics. Stanley,
R. P. Enumerative
Combinatorics, Vol. 1. Stanley, R. P. Enumerative
Combinatorics, Vol. 2. Street, A. P. and Wallis, W. D. Combinatorial
Theory: An Introduction. Tucker, A. Applied
Combinatorics, 3rd ed. van Lint, J. H.
and Wilson, R. M. A
Course in Combinatorics. Weisstein,
E. W. "Books about Combinatorics." http://www.ericweisstein.com/encyclopedias/books/Combinatorics.html . Wilf,
H. S. Combinatorial
Algorithms: An Update. Referenced
on Wolfram|Alpha Combinatorics
Cite this as:
Weisstein, Eric W. "Combinatorics." From
MathWorld https://mathworld.wolfram.com/Combinatorics.html
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