INCIDENCE FUNCTION Meaning and
Definition
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The term "incidence function" refers to a mathematical concept utilized in various fields, particularly in combinatorics and graph theory. An incidence function is a mapping or relationship that associates two sets, typically a set of objects and a set of properties, determining whether each object possesses a particular property or not.
In combinatorics, an incidence function may describe the presence or absence of an object within a particular subset or structure. For instance, in the study of finite geometries, the incidence function can indicate which points lie on a given line or which lines intersect at a particular point.
In graph theory, an incidence function is commonly used to describe the relationship between vertices and edges in a graph. It assigns a value of either 0 or 1 to each pair of vertices and edges, indicating whether the vertex is incident to the edge or not. This function helps determine the connectivity and adjacency properties of a graph.
Incidence functions can also be utilized in epidemiology to analyze the relationship between individuals and diseases. Here, the function determines whether a person has been affected by a specific disease or condition.
Overall, an incidence function acts as a mapping that establishes the presence or absence of a property or relationship between two sets, making it a vital tool in various mathematical and scientific disciplines.
Etymology of INCIDENCE FUNCTION
The etymology of the word "incidence function" can be traced back to Latin and French origins.
The term "incidence" comes from the Latin word "incidentia", which means "a falling upon" or "occurrence". In mathematics, "incidence" refers to the relationship between elements of a set, typically representing points and lines, or points and planes.
The word "function" is derived from the Latin word "functio", meaning "performance" or "execution". In mathematics, a function describes a specific relationship between input values and output values.
Therefore, when combined to form the term "incidence function", it refers to a mathematical function that describes the relationship between elements in a set, such as the incidence of points and lines, or points and planes in geometry.
