Gnumber

Gnumber is a term used in multiple disciplines to denote a numeric invariant or identifier associated with a concrete object. There is no universally accepted definition, and the precise meaning depends on the context and the author.

In mathematics and discrete mathematics, Gnumber has been used to denote several different ideas. In graph theory and combinatorics, some authors define the Gnumber of a graph as the minimum integer k such that the object satisfies a particular property P_k (for example, a specific kind of coloring or covering). In algebra, the term has appeared as an informal name for the minimal number of generators required to generate a given structure, such as a module or ideal, though this is more commonly called the generator number or rank in standard terminology. In dynamical systems, some works use Gnumber to refer to a growth bound associated with an orbit under a transformation.

In computing and information theory, Gnumber has been used as a label for resource-related measures in theoretical models or as a generator value in cryptographic schemes, again with definitions varying by model. In practice, researchers tend to define Gnumber explicitly in each work, and readers should consult the specific definition when encountering the term. Because of its ambiguous usage, Gnumber is often accompanied by contextual qualifiers or a formal definition within the source.

See also: chromatic number, Grundy number, generator, rank (algebra), growth rate.