Cyclic (mathematics)
Encyclopedia
There are many terms in mathematics that begin with cyclic:
- Cyclic chain rule, for derivatives, used in thermodynamics
- Cyclic code, linear codes closed under cyclic permutations
- Cyclic convolution, a method of combining periodic functions
- Cycle decomposition (graph theory)Cycle decomposition (graph theory)In graph theory, a cycle decomposition is a partitioning of the vertices of a graph into subsets, such that the vertices in each subset lie on a cycle....
- Cycle decomposition (group theory)
- Cyclic extension, a field extension with cyclic Galois group
- Cycle graphCycle graphIn graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices connected in a closed chain. The cycle graph with n vertices is called Cn...
or cyclic graph is a connected, 2-regular graph:- Cycle graph (algebra)Cycle graph (algebra)In group theory, a sub-field of abstract algebra, a group cycle graph illustrates the various cycles of a group and is particularly useful in visualizing the structure of small finite groups...
, a diagram representing the cycles determined by taking powers of group elements - Circulant graphCirculant graphIn graph theory, a circulant graph is an undirected graph that has a cyclic group of symmetries that includes a symmetry taking any vertex to any other vertex.-Equivalent definitions:Circulant graphs can be described in several equivalent ways:...
, a graph whose adjacency matrix is circulant - Cycle (graph theory)Cycle (graph theory)In graph theory, the term cycle may refer to a closed path. If repeated vertices are allowed, it is more often called a closed walk. If the path is a simple path, with no repeated vertices or edges other than the starting and ending vertices, it may also be called a simple cycle, circuit, circle,...
, a nontrivial path from a node to itself
- Cycle graph (algebra)
- Cyclic groupCyclic groupIn group theory, a cyclic group is a group that can be generated by a single element, in the sense that the group has an element g such that, when written multiplicatively, every element of the group is a power of g .-Definition:A group G is called cyclic if there exists an element g...
, a group generated by a single element - Cyclic homologyCyclic homologyIn homological algebra, cyclic homology and cyclic cohomology are homology theories for associative algebras introduced by Alain Connes around 1980, which play an important role in his noncommutative geometry...
, an approximation of K-theory used in non-commutative differential geometry - Cyclic moduleCyclic moduleIn mathematics, more specifically in ring theory, a cyclic module is a module over a ring which is generated by one element. The term is by analogy with cyclic groups, that is groups which are generated by one element.- Definition :...
, a module generated by a single element - Cyclic notation, a way of writing permutations
- Cyclic numberCyclic numberA cyclic number is an integer in which cyclic permutations of the digits are successive multiples of the number. The most widely known is 142857:For example:Multiples of these fractions exhibit cyclic permutation:...
, a number such that cyclic permutations of the digits are successive multiples of the number - Cyclic order, a binary relation for doubly linked lists
- Cyclic permutationCyclic permutationA cyclic permutation or circular permutation is a permutation built from one or more sets of elements in cyclic order.The notion "cyclic permutation" is used in different, but related ways:- Definition 1 :right|mapping of permutation...
, a permutation with one nontrivial orbit - Cyclic polygon, a polygon which can be given a circumscribed circle
- Cyclic shift, also known as circular shift
- Cyclic symmetry, n-fold rotational symmetry of 3-dimensional space