combinatorics
combinatorics (kŏm´bənətôr´Ĭks) or combinatorial analysis (kŏm´bĬnətôr´ēəl), sometimes called the science of counting, the branch of mathematics concerned with the selection, arrangement, and operation of elements within sets. Combinatorial theory deals with existence (does a particular arrangement exist?), enumeration (how many such arrangements are there?) and structure (what are the properties of each arrangement?). It has applications in such diverse areas as managing computer and telecommunication networks, predicting poker hands, dividing tasks among workers, and finding a pair of socks in a drawer. Because combinatorics deals with concrete problems by limiting itself to finite collections of discrete objects, as opposed to the more common, continuous mathematics, it has neither standard algebraic manipulations nor a systematic problemsolving framework. Instead it relies upon the logical analysis of possibilities for each new problem, breaking the problem into a series of steps and substeps. Combinatorics has its roots in the 17th and 18thcentury attempts to analyze the odds of winning at games of chance. The advent of computers in the 20th cent. made possible the highspeed calculation required to analyze the multitude of possibilities inherent in a combinatorial approach to largescale statistical testing and analysis. Branches of combinatorics include graph theory and combinations and permutations.
See A. Slomson, An Introduction to Combinatorics (1991); A. Tucker, Applied Combinatorics (3d ed. 1994); R. A. Brualdi, Introductory Combinatorics (3d ed. 1997); M. Hall, Combinatorial Theory (2d ed. 1998); R. P. Stanley, Enumerative Combinatorics (1999).
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"combinatorics." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. 19 Apr. 2018 <http://www.encyclopedia.com>.
"combinatorics." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (April 19, 2018). http://www.encyclopedia.com/reference/encyclopediasalmanacstranscriptsandmaps/combinatorics
"combinatorics." The Columbia Encyclopedia, 6th ed.. . Retrieved April 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/reference/encyclopediasalmanacstranscriptsandmaps/combinatorics
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.
combinatorics
combinatorics The branch of mathematics concerned with the counting problems and enumeration problems associated with such topics as combinations, permutations, number theory, arithmetic, and the theory of graphs, groups, and other discrete structures. Induction, recursion, and recurrence relations tend to play a significant role in much of this work. In computational combinatorics the underlying theory is applied to algorithms of any kind.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"combinatorics." A Dictionary of Computing. . Encyclopedia.com. 19 Apr. 2018 <http://www.encyclopedia.com>.
"combinatorics." A Dictionary of Computing. . Encyclopedia.com. (April 19, 2018). http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/combinatorics
"combinatorics." A Dictionary of Computing. . Retrieved April 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/combinatorics
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.