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The principle can be viewed as an example of the sieve method extensively used in number theory and is sometimes referred to as the sieve formula. [ 4 ] As finite probabilities are computed as counts relative to the cardinality of the probability space , the formulas for the principle of inclusion–exclusion remain valid when the cardinalities ...
The choosability (or list colorability or list chromatic number) ch(G) of a graph G is the least number k such that G is k-choosable. More generally, for a function f assigning a positive integer f(v) to each vertex v, a graph G is f-choosable (or f-list-colorable) if it has a list coloring no matter how one assigns a list of f(v) colors to ...
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
In mathematics education, a representation is a way of encoding an idea or a relationship, and can be both internal (e.g., mental construct) and external (e.g., graph). Thus multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate ...
An example of the kind of differences that can be tested for is non-normality of the population distribution. Recurrence plot : In descriptive statistics and chaos theory, a recurrence plot (RP) is a plot showing, for a given moment in time, the times at which a phase space. In other words, it is a graph of
A weighted graph or a network [9] [10] is a graph in which a number (the weight) is assigned to each edge. [11] Such weights might represent for example costs, lengths or capacities, depending on the problem at hand. Such graphs arise in many contexts, for example in shortest path problems such as the traveling salesman problem.
Every planar graph has cop number at most three. [1] More generally, every graph has cop number at most proportional to its genus. [7] However, the best known lower bound for the cop number in terms of the genus is approximately the square root of the genus, which is far from the upper bound when the genus is large. [2]
The complete list of all free trees on 2, 3, and 4 labeled vertices: = tree with 2 vertices, = trees with 3 vertices, and = trees with 4 vertices.. In combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the ...