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Что (кто) такое extremal basis - определение

Extremal graph

Standard basis

BASIS OF EUCLIDEAN SPACE CONSISTING OF ONE-HOT VECTORS

Standard bases; Standard basis vector; Kronecker basis; Standard unit vector

In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as \mathbb{R}^n or \mathbb{C}^n) is the set of vectors whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane \mathbb{R}^2 formed by the pairs of real numbers, the standard basis is formed by the vectors

https://en.wikipedia.org/wiki/Standard_basis

Basis (universal algebra)

STRUCTURE INSIDE OF SOME (UNIVERSAL) ALGEBRAS, WHICH ARE CALLED FREE ALGEBRAS. IT GENERATES ALL ALGEBRA ELEMENTS FROM ITS OWN ELEMENTS BY THE ALGEBRA OPERATIONS IN AN INDEPENDENT MANNER

Basis (Universal Algebra)

In universal algebra, a basis is a structure inside of some (universal) algebras, which are called free algebras. It generates all algebra elements from its own elements by the algebra operations in an independent manner.

https://en.wikipedia.org/wiki/Basis_(universal_algebra)

Dual basis

BASIS ON A DUAL VECTOR SPACE CANONICALLY ASSOCIATED TO A BASIS ON THE ORIGINAL VECTOR SPACE

Reciprocal basis

In linear algebra, given a vector space V with a basis B of vectors indexed by an index set I (the cardinality of I is the dimensionality of V), the dual set of B is a set B∗ of vectors in the dual space V∗ with the same index set I such that B and B∗ form a biorthogonal system. The dual set is always linearly independent but does not necessarily span V∗.

https://en.wikipedia.org/wiki/Dual_basis

Википедия

Extremal graph theory

Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence, extremal graph theory studies how global properties of a graph influence local substructure. Results in extremal graph theory deal with quantitative connections between various graph properties, both global (such as the number of vertices and edges) and local (such as the existence of specific subgraphs), and problems in extremal graph theory can often be formulated as optimization problems: how big or small a parameter of a graph can be, given some constraints that the graph has to satisfy? A graph that is an optimal solution to such an optimization problem is called an extremal graph, and extremal graphs are important objects of study in extremal graph theory.

Extremal graph theory is closely related to fields such as Ramsey theory, spectral graph theory, computational complexity theory, and additive combinatorics, and frequently employs the probabilistic method.

https://en.wikipedia.org/wiki/Extremal graph theory