Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative...
Combinatorics - Wikipedia
History of combinatorics
The history of combinatorics is an area of study within the history of mathematics. Its focus ranges from antiquity to modern times.
The earliest known connection to combinatorics comes from the ...
History of combinatorics - Wikipedia
Enumerative combinatorics
Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and countin...
Analytic combinatorics
In mathematics, analytic combinatorics is one of the many techniques of counting combinatorial objects. It uses the internal structure of the objects to derive formulas for their generating functions...
Partition (number theory)
In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order o...
Partition (number theory) - Wikipedia
Graph theory
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A "graph" in this context is made up of "v...
Combinatorial design
Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concep...
Finite geometry
A finite geometry is any geometric system that has only a finite number of points.The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry ba...
Finite geometry - Wikipedia
Order theory
Order theory is a branch of mathematics which investigates our intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than tha...
Matroid theory
In combinatorics, a branch of mathematics, a matroid /ˈmeɪtrɔɪd/ is a structure that captures and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to defi...
Extremal combinatorics
Extremal combinatorics is a field of combinatorics, which is itself a part of mathematics. Extremal combinatorics studies how large or how small a collection of finite objects (numbers, graphs, vector...
Probabilistic method
The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. It works ...
Algebraic combinatorics
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies c...
Combinatorics on words
Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages. The subject looks at letters or symbols, and the s...
Geometric combinatorics
Geometric combinatorics is a branch of mathematics in general and combinatorics in particular. It includes a number of subareas such as polyhedral combinatorics (the study of faces of convex polyhedr...
Topological combinatorics
The discipline of combinatorial topology used combinatorial concepts in topology and in the early 20th century this turned into the field of algebraic topology.In 1978 the situation was reversed – met...
Arithmetic combinatorics
In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.
Arithmetic combinatorics is about combinatorial estim...
Infinitary combinatorics
In mathematics, infinitary combinatorics, or combinatorial set theory, is an extension of ideas in combinatorics to infinite sets.Some of the things studied include continuous graphs and trees, extens...
Combinatorial game theory
Combinatorial game theory (CGT) is a branch of applied mathematics and theoretical computer science that studies sequential games with perfect information, that is, two-player games which have a posit...
Combinatorial game theory - Wikipedia
Design theory
Design theory covers the methods, strategies, research and analysis of the term design. Design theory underpins the concept of, and reflection upon, creative work.Design theory, as well as design, is ...
Incidence geometry
In mathematics, incidence geometry is the study of incidence structures. A geometry such as the Euclidean plane is a complicated object involving concepts such as length, angles, continuity, betweenne...
Incidence geometry - Wikipedia
Integer sequence
In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers.An integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a re...
Permutation
In mathematics, the notion of permutation relates to the act of rearranging, or permuting, all the members of a set into some sequence or order (unlike combinations, which are selections of some membe...
Q-analog
Roughly speaking, in mathematics, specifically in the areas of combinatorics and special functions, a q-analog of a theorem, identity or expression is a generalization involving a new parameter q that...
Ramsey theory
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear. Problems in Ramsey theory ty...
Ramsey theory - Wikipedia