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Q-analog

In mathematics, a q-analog of a theorem, identity or expression is a generalization involving a new parameter q that returns the original theorem, identity or expression in the limit as. [1]

Algebraic group

In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inversion operations are given by regular maps on the variety.

In mathematics, an Apollonian gasket or Apollonian net is a fractal generated starting from a triple of circles, each tangent to the other two, and successively filling in more circles, each tangent to another three.

Basic hypergeometric series

In mathematics, basic hypergeometric series, or hypergeometric q-series, are ''q''-analogue generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series.

Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.

Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.

Elliptic curve

In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form which is non-singular; that is, the curve has no cusps or self-intersections.

Elliptic integral

In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse.

Entropy

In statistical mechanics, entropy is an extensive property of a thermodynamic system.

Ergodic theory

Ergodic theory (Greek: έργον ergon "work", όδος hodos "way") is a branch of mathematics that studies dynamical systems with an invariant measure and related problems.

Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.

Field with one element

In mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could exist.

Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

Fractal

In mathematics, a fractal is an abstract object used to describe and simulate naturally occurring objects.

Fuchsian group

In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,'''R''').

Gaussian binomial coefficient

In mathematics, the Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian polynomials, or q-binomial coefficients) are ''q''-analogs of the binomial coefficients.

Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

Indra's Pearls (book)

Indra's Pearls: The Vision of Felix Klein is a geometry book written by David Mumford, Caroline Series and David Wright, and published by Cambridge University Press in 2002 and 2015.

Inversion (discrete mathematics)

In computer science and discrete mathematics a sequence has an inversion where two of its elements are out of their natural order.

Limit (mathematics)

In mathematics, a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value.

List of q-analogs

This is a list of ''q''-analogs in mathematics and related fields.

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

MathWorld

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.

Modular form

In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition.

Modular group

In mathematics, the modular group is the projective special linear group PSL(2,Z) of 2 x 2 matrices with integer coefficients and unit determinant.

Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

Physical Review A

Physical Review A (also known as PRA) is a monthly peer-reviewed scientific journal published by the American Physical Society covering atomic, molecular, and optical physics and quantum information.

Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

Prime power

In mathematics, a prime power is a positive integer power of a single prime number.

Q-exponential

In combinatorial mathematics, a q-exponential is a ''q''-analog of the exponential function, namely the eigenfunction of a q-derivative.

Q-Pochhammer symbol

In mathematics, in the area of combinatorics, a q-Pochhammer symbol, also called a q-shifted factorial, is a ''q''-analog of the Pochhammer symbol.

Quantum group

In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebras with additional structure.

Ramsey theory

Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear.

Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.

Special functions

Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications.

Sperner's theorem

Sperner's theorem, in discrete mathematics, describes the largest possible families of finite sets none of which contain any other sets in the family.

Stirling number

In mathematics, Stirling numbers arise in a variety of analytic and combinatorial problems.

String theory

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.

Superalgebra

In mathematics and theoretical physics, a superalgebra is a Z2-graded algebra.

Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

Weyl group

In mathematics, in particular the theory of Lie algebras, the Weyl group of a root system Φ is a subgroup of the isometry group of the root system.

Young tableau

In mathematics, a Young tableau (plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus.

References

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