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 of their summands are considered the same partition. (If order matters, the sum becomes a composition.)For example, 4 can be partitioned in five distinct ways:

In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent.That is, it is a set of vertices such that for every two vertices in , there is no edge connecting the two. Equivalently, each edge in the graph has at most one endpoint in .A set is independent if and only if it is a clique in the graph's complement.

Valence shell electron pair repulsion (VSEPR) theory (/ ˈ v ɛ s p ər, v ə ˈ s ɛ p ər / VESP-ər,: 410 və-SEP-ər), is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. It is also named the Gillespie-Nyholm theory after its two main developers, Ronald Gillespie and Ronald Nyholm.

In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exists a pair of integers (p, q) with q > 1 such that < | | <. Liouville numbers are "almost rational", and can thus be approximated "quite closely" by sequences of rational numbers. They are precisely those transcendental numbers that can be more closely …

Definition and properties. Let be a natural number. We define the Kaprekar function for base > and power >,: to be the following: , = +, where = and = A natural number is a -Kaprekar number if it is a fixed point for ,, which occurs if , =. and are trivial Kaprekar numbers for all and , all other Kaprekar numbers are nontrivial Kaprekar numbers.. For example, in base 10, 45 is a 2 …

In the mathematical area of graph theory, a clique (/ ˈ k l iː k / or / ˈ k l ɪ k /) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent.That is, a clique of a graph is an induced subgraph of that is complete.Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on ...

In the mathematical field of group theory, Lagrange's theorem is a theorem that states that for any finite group G, the order (number of elements) of every subgroup of G divides the order of G.The theorem is named after Joseph-Louis Lagrange.The following variant states that for a subgroup of a finite group , not only | | / | | is an integer, but also that its value is the index [:], …

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.Every point of a number line is assumed to correspond to a real number, and every real number to a point.. The integers are often shown as specially-marked points evenly spaced on the line. Although the image only shows the integers from –3 …

Institutional Theory. The effective number of parties can be predicted with the seat product model as = /, where M is the district magnitude and S is the assembly size.. Effective number of parties by country. For individual countries the values of effective number of number of parliamentary parties (ENPP) for the last available election is shown. Some of the highest …

Definition. The definition of Rayo's number is a variation on the definition: The smallest number bigger than any finite number named by an expression in the language of first-order set theory with a googol symbols or less.. Specifically, an initial version of the definition, which was later clarified, read "The smallest number bigger than any number that can be named by an …