Mathematics and statistics

L-infinity

L-infinity, written L^∞, is the Banach space of essentially bounded measurable functions on a measure space, normed by the essential supremum and forming the endpoint of the L^p family.

L-system

An L-system, or Lindenmayer system, is a parallel string-rewriting formalism in which every symbol is rewritten at each step, introduced by Aristid Lindenmayer in 1968 to model plant development.

L'Hôpital's rule

L'Hôpital's rule, also called De L'Hospital's Rule, is a calculus theorem for finding limits of quotients in indeterminate forms by differentiating the numerator and denominator separately.

The labeled enumeration theorem, also called the fundamental theorem of combinatorial enumeration, translates constructions on labeled combinatorial structures into equations on their exponential generating functions, the labeled counterpart of Pólya's theorem.

Labour Force Survey

The Labour Force Survey (LFS) is the UK's largest household survey, run by the Office for National Statistics since 1973, providing the official measures of employment and unemployment.

Ladder graph

The ladder graph Lₙ is the Cartesian product of two path graphs, P₂ and Pₙ, forming two rails joined by n rungs like a ladder.

Lagrange multipliers

Lagrange multipliers are auxiliary variables used to find the extrema of a function subject to equality constraints, introduced by Joseph-Louis Lagrange in the late 18th century.

Lagrange polynomial

A Lagrange polynomial, also called Lagrange interpolation or the Lagrange form, is a basis polynomial used in numerical analysis to build the unique polynomial through n+1 data points.

Lagrange's four-square theorem

Lagrange's four-square theorem, also known as Bachet's conjecture, states that every positive integer is a sum of at most four squares of integers, first proved by Lagrange in 1770.

Lagrange's theorem (group theory)

Lagrange's theorem, also called Lagrange's Group Theorem, is a result in group theory stating that the order of any subgroup of a finite group divides the order of the group.

Lagrangian relaxation

Lagrangian relaxation is an optimization method, named by Geoffrion in 1974, that removes difficult constraints and penalizes their violation, producing bounds used inside branch and bound.

Laguerre polynomials

The Laguerre polynomials, also known as Sonin polynomials, are a family of classical orthogonal polynomials introduced by Edmond Laguerre in 1879, used in hydrogen-atom wavefunctions and Gauss–Laguerre quadrature.

Lakh (लाख)

Lakh (लाख), also spelled lac, is a unit in the Indian numbering system equal to one hundred thousand, the standard large-number word in South Asian finance and everyday speech.

Laman graph

A Laman graph is a graph on n vertices with exactly 2n − 3 edges whose subsets stay sparse, making it minimally rigid in the plane by Laman's 1970 theorem.

Lambda calculus

The lambda calculus, also written λ-calculus, is a formal system invented by Alonzo Church in the 1930s that expresses computation through function definition and application, computing exactly what Turing machines compute.

Lambda cube

The lambda cube is Henk Barendregt's arrangement of eight typed lambda calculi, formed from the simply typed lambda calculus by adding polymorphism, type operators, and dependent types.

Lambek calculus

The Lambek calculus, or syntactic calculus, is a substructural logic introduced by Joachim Lambek in 1958, in which grammatical well-formedness is decided by logical derivability over syntactic types.

Lambert W function

The Lambert W function, also called the omega function, is the multivalued inverse of w e^w, with infinitely many branches, two of which take real values.

Lanchester's laws

Lanchester's laws, or the Lanchester equations, are mathematical models of combat attrition proposed by Frederick Lanchester in 1916, with a square law for aimed fire and a linear law for duels.

Lanczos algorithm

The Lanczos algorithm, also called the Lanczos method, is an iterative method introduced by Cornelius Lanczos in 1950 for finding extreme eigenvalues of large sparse symmetric matrices.

Landau's problems

Landau's problems, or Landau's conjectures, are four unsolved statements about prime numbers, named by Edmund Landau at the 1912 International Congress of Mathematicians in Cambridge as unattackable.

Landmark analysis

Landmark analysis is a survival-analysis method that estimates survival or treatment effect after a fixed landmark time, correcting the immortal time bias in responder comparisons.

Landweber iteration

Landweber iteration is a gradient-descent method for solving ill-posed linear inverse problems, introduced by Louis Landweber in 1951 and used in image deblurring and tomography.

Langevin algorithm

The Langevin algorithm is a Markov chain Monte Carlo method that samples a probability distribution by following the gradient of its log-density with added Gaussian noise.

Langlands dual group

The Langlands dual group of a reductive group G, introduced by Robert Langlands in the late 1960s, is the reductive group obtained by exchanging characters with cocharacters and roots with coroots.

Langlands program

The Langlands program, also known as the Langlands conjectures, is a collection of conjectures proposed by Robert Langlands in 1967 linking Galois representations and automorphic forms.

Langlands–Shahidi method

The Langlands–Shahidi method is a technique in automorphic forms that proves analytic continuation and functional equations for automorphic L-functions by studying constant terms of Eisenstein series.

Langton's ant

Langton's ant is a two-dimensional cellular automaton invented by Christopher G. Langton in 1986, in which an ant following two simple rules builds an endless diagonal highway after about 10,000 chaotic steps.

LAPACK

LAPACK (Linear Algebra Package) is a freely available Fortran library, first released in 1992, for solving linear systems, least-squares, eigenvalue, and singular value problems for dense and banded matrices.