Combinatorics
The branch of mathematics studying the enumeration, combination, and permutation of sets of elements and themathematical relations which characterize these properties.
See also Antichain, Chain, Dilworth's Lemma, Diversity Condition, Erdös-SzekeresTheorem, Inclusion-Exclusion Principle, Kirkman's Schoolgirl Problem, KirkmanTriple System, Length (Partial Order), Partial Order, Pigeonhole Principle, Ramsey's Theorem,Schröder-Bernstein Theorem, Schur's Lemma, Sperner's Theorem,Total Order, van der Waerden's Theorem, Width (Partial Order)
References
Abramowitz, M. and Stegun, C. A. (Eds.). ``Combinatorial Analysis.'' Ch. 24 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 821-8827, 1972. Aigner, M. Combinatorial Theory. New York: Springer-Verlag, 1997. Bellman, R. and Hall, M. Combinatorial Analysis. Amer. Math. Soc., 1979. 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. Brown, K. S. ``Combinatorics.''http://www.seanet.com/~ksbrown/icombina.htm. 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. CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, 1996. Comtet, L. Advanced Combinatorics. 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. Electronic Journal of Combinatorics. http://www.combinatorics.org/previous_volumes.html. Eppstein, D. ``Combinatorial Geometry.''http://www.ics.uci.edu/~eppstein/junkyard/combinatorial.html. Erickson, M. J. Introduction to Combinatorics. New York: Wiley, 1996. Fields, J. ``On-Line Dictionary of Combinatorics.'' http://math.uic.edu/~fields/dic/. Godsil, C. D. ``Problems in Algebraic Combinatorics.'' Electronic J. Combinatorics 2, F1 1-20, 1995.http://www.combinatorics.org/Volume_2/volume2.html#F1. 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. Hall, M. Jr. Combinatorial Theory, 2nd ed. New York: Wiley, 1986. Knuth, D. E. (Ed.). Stable Marriage and Its Relation to Other Combinatorial Problems. Providence, RI: Amer. Math. Soc., 1997. Kucera, 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. New York: Chelsea, 1960. Nijenhuis, A. and Wilf, H. Combinatorial Algorithms for Computers and Calculators, 2nd ed. New York: Academic Press, 1978. 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. Rota, G.-C. (Ed.). Studies in Combinatorics. Providence, RI: Math. Assoc. Amer., 1978. Ruskey, F. ``The (Combinatorial) Object Server.'' http://sue.csc.uvic.ca/~cos/. Ryser, H. J. Combinatorial Mathematics. Buffalo, NY: Math. Assoc. Amer., 1963. Skiena, S. 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. 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. Wilf, H. S. Combinatorial Algorithms: An Update. Philadelphia, PA: SIAM, 1989.
Combinatorics
- Doublet Function
- Doubly Even Number
- Doubly Magic Square
- Dougall-Ramanujan Identity
- Dougall's Theorem
- Doughnut
- Douglas-Neumann Theorem
- Dovetailing Problem
- Dowker Notation
- Down Arrow Notation
- Dozen
- Dragon Curve
- Dragon Fractal
- Draughts
- Drinfeld's Symmetric Space
- Droz-Farny Circles
- Drum
- D-Statistic
- D-Triangle
- Dual Basis
- Dual Bivector
- Dual Graph
- Duality Principle
- Duality Theorem
- Dual Map