Combinatorial class

Combinatorial class

In combinatorics, a combinatorial class (or simply class) is an equivalence class of sets that have the same counting sequence. Although the elements of these equivalent sets may have very different definitions and semantics, combinatorics is concerned only with the number of elements of a given size. Therefore, knowledge about one set in the class can be applied directly to other sets in the class.

For example, the set of triangulations of polygons is combinatorially isomorphic to the set of general rooted plane trees. Although these sets certainly describe different things, they have the same counting sequence, namely the Catalan numbers.

See also


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Combinatorial meta-analysis — (CMA) is the study of the behaviour of statistical properties of combinations of studies from a meta analytic dataset (typically in social science research). In an article that develops the notion of gravity in the context of meta analysis, Dr.… …   Wikipedia

  • Combinatorial species — In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for analysing discrete structures in terms of generating functions. Examples of discrete structures are (finite) graphs, permutations, trees, and… …   Wikipedia

  • Combinatorial game theory — This article is about the theory of combinatorial games. For the theory that includes games of chance and games of imperfect knowledge, see Game theory. Mathematicians playing Konane at a Combinatorial game theory workshop (for technical content …   Wikipedia

  • Combinatorial explosion — For other uses, see Combinatorial explosion (communication). In mathematics a combinatorial explosion describes the effect of functions that grow very rapidly as a result of combinatorial considerations.[1] Examples of such functions include the… …   Wikipedia

  • Fundamental theorem of combinatorial enumeration — The fundamental theorem of combinatorial enumeration is a theorem in combinatorics that solves the enumeration problem of labelled and unlabelled combinatorial classes. The unlabelled case is based on the Pólya enumeration theorem.This theorem is …   Wikipedia

  • List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

  • Symbolic combinatorics — in mathematics is a technique of analytic combinatorics that uses symbolic representations of combinatorial classes to derive their generating functions. The underlying mathematics, including the Pólya enumeration theorem, are explained on the… …   Wikipedia

  • Stirling numbers and exponential generating functions — The use of exponential generating functions or EGFs to study the properties of Stirling numbers is a classical exercise in combinatorics and possibly the canonical example of how symbolic combinatorics, the method that encapsulates the… …   Wikipedia

  • Random permutation statistics — The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations. Suppose, for example,… …   Wikipedia

  • List of combinatorics topics — This is a list of combinatorics topics.A few decades ago it might have been said that combinatorics is little more than a way to classify poorly understood problems, and some standard remedies. Great progress has been made since 1960.This page is …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”