Glossary: L

Definitions in this project whose names start with L. The whole glossary has the other sections.

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L def

$L_n$ is the least common multiple of $\{1,\ldots,n\}$. · Erdos291.L

L def

L x is the maximal number of square partial products of a sequence $1\leq a_1<\cdots<a_k\leq x$. · Erdos437.L

L def

The Erdős primitive-set game length on $\{2, \dots, n\}$. · Erdos872.L

l def

The 3-adic valuation of $n(n+1)$. · Erdos933.l

l def

l w is the word obtained by reversing w and subtracting 1 from every term. · OeisA108081.l

l abbrev

Abbreviation for the average independence number of the neighborhoods. · SimpleGraph.l

L10_local def

The space-time $L^10$ norm, restricted to the time interval $[-l,l]$. · NLSCritical.L10_local

l_avg abbrev

The same quantity under a different name, used in some conjectures. · SimpleGraph.l_avg

lambda def

The numbers $$ \lambda_n := \sum_{\rho}\left(1 - \left(1 - \frac{1}{\rho}\right)^n\right) $$ appearing in Li's criterion, summing over the nontrivial zeros $\rho$ of the Riemann zeta function. · RiemannHypothesis.lambda

landauConstant def

The Landau constant $L$ is the largest radius such that every holomorphic function on the unit disk with $f'(0) = 1$ has a disk of that radius contained in its image. · Bloch.landauConstant

landauRadius def

The Landau radius $L_f$ of a function $f$ is the supremum of radii of disks contained in the image of the unit disk under $f$. Takes values in ℝ≥0∞ so that functions with unbounded image correctly get radius ⊤. · Bloch.landauRadius

largeOmegaIntervalLength def

The greatest length of an interval in $[x,2x]$ on which $\omega(n) > \log\log n$ everywhere. · Erdos452.largeOmegaIntervalLength

LargestAdmissibleCardinality def

The largest subset $A \subset \mathbb{F}_7^n$ for which $A - A$ intersects $\{-1, 0, 1\}^n$ only at $0$. · Green38.LargestAdmissibleCardinality

LargeSteinerSystemWitness structure

A constructive witness for a large Steiner system: concrete values of $n$, $k$, $t$ satisfying $n > k > t > 5$, $t < 10$, $n < 200$, together with an explicit Steiner system. · SteinerSystems.LargeSteinerSystemWitness

largestInducedBipartiteSubgraphSize def

largestInducedBipartiteSubgraphSize G is the size of a largest induced bipartite subgraph of G. · SimpleGraph.largestInducedBipartiteSubgraphSize

largestInducedForestSize def

largestInducedForestSize G is the size of a largest induced forest of G. · SimpleGraph.largestInducedForestSize

largestInducedPathSize def

The size of a largest induced path of $G$, as a natural number. · WrittenOnTheWallII.GraphConjecture314.largestInducedPathSize

largestInducedTreeSize def

largestInducedTreeSize G is the number of vertices in a largest induced subtree of G. A tree is a connected acyclic graph; an induced tree is an induced subgraph that is a tree. · SimpleGraph.largestInducedTreeSize

LargestPrimeRepeated def

LargestPrimeRepeated u v means that $1 \leq u \leq v$ and the largest prime $p$ dividing $\prod_{u \leq m \leq v} m$ appears in it with exponent at least $2$, that is $p^2$ divides the product. · Erdos382.LargestPrimeRepeated

latexDocstringLinter def

The linter checking markup in docstrings. · LatexDocstringLinter.latexDocstringLinter

LatinSquare structure

A latin square of order n is an n × n matrix with entries in Fin n such that each symbol appears exactly once in every row and exactly once in every column. · LatinSquare

lbMeasure abbrev

The standard Lebesgue measure on ℝ². · Mathoverflow34145.lbMeasure

lcm_upto def

The least common multiple of the integers in the set $\{1, \dots, n\}$. · Erdos458.lcm_upto

lcmInterval def

The least common multiple of ${n+1, \dotsc, n+k}$. · Finset.lcmInterval

lcmMatrix def

The $n \times n$ matrix with entry $(i,j)$ equal to $1/\operatorname{lcm}(i+1, j+1)$ over $\mathbb{Q}$. · OeisA60841.lcmMatrix

leastCongruentPrime def

leastCongruentPrime a d is the least prime congruent to a modulo d. · Erdos971.leastCongruentPrime

leastPrimeAbove def

The least prime strictly greater than n, found in the Bertrand interval. · OeisA67836.leastPrimeAbove

left_factorial def

Left factorial of n $$!n = 0! + 1! + 2! + \dots + (n-1)!$$ · Kurepa.left_factorial

leftIndex def

The embedding of the first $m$ indices into $\mathrm{Fin}\, n$. · OpenQuantumProblem35.leftIndex

legalMoves def

The legal moves from a position: unclaimed elements whose insertion preserves primitiveness. · Erdos872.legalMoves

lehmerPolynomial def

def lehmerPolynomial : ℤ[X] · LehmerMahlerMeasureProblem.lehmerPolynomial

lemniscate def

The open unit lemniscate $E = \{z : \lvert f(z)\rvert < 1\}$ of a complex polynomial. · Erdos1046.lemniscate

lemniscate def

The lemniscate $\{z \in \mathbb{C} : \lvert p(z)\rvert = 1\}$ of a complex polynomial $p$. · Erdos114.lemniscate

lemniscateLength def

The length of the lemniscate of $p$, as its one-dimensional Hausdorff measure. · Erdos114.lemniscateLength

length def

The length of a subset $s$ of $\mathbb{C}$ is defined to be its 1-dimensional Hausdorff measure $\mathcal{H}^1(s)$. · Erdos1041.length

length def

The length of a cycle, its number of edges. · SimpleGraph.Cycle.length

levelSet def

The set $\{ z \in \mathbb{C} : \lvert f(z)\rvert\leq 1\}$ · Erdos1043.levelSet

lieDeriv def

The left invariant derivative along X as a ℂ-linear endomorphism of the C^∞ functions on GL n ℝ. · Matrix.GeneralLinearGroup.lieDeriv

lieDerivC def

The action of the complexified Lie algebra 𝔤𝔩 n ℂ of GL n ℝ on the C^∞ functions: X + i Y acts as lieDeriv X + i • lieDeriv Y. · Matrix.GeneralLinearGroup.lieDerivC

lieDerivFun def

The left invariant derivative of φ along X: differentiate φ along the one-parameter subgroup t ↦ exp (t • X) acting on the right, · Matrix.GeneralLinearGroup.lieDerivFun

lieDerivHom def

The action of 𝔤𝔩 n ℂ on the C^∞ functions on GL n ℝ by left invariant differential operators, as a homomorphism of ℂ-Lie algebras. · Matrix.GeneralLinearGroup.lieDerivHom

LieGroupPresentation structure

A continuous group isomorphism from G to an n-dimensional real-analytic Lie group. The Lie group is not assumed to be second countable. · LieGroupPresentation

limitPointSet def

The set $\{1\} \cup \{1+1/k : k \geq 1\}$. · Erdos419.limitPointSet

limitPointSet def

The set $S$ of limit points of $\frac{p_{n+1}-p_n}{\log n}$. · Erdos5.limitPointSet

limitValue def

Conjectured limit value for $F(n+1, L) / F(n, L)$. · OeisA181546.limitValue

linearFactor def

The homogeneous linear factor determined by a lifted direction. · AtiyahSutcliffe.linearFactor

linearIndependenceNumber def

Smallest independence number of a linear three-uniform hypergraph on n vertices. · Hypergraph.linearIndependenceNumber

linesWithPointsFor def

The set of lines in $\mathbb{R}^2$ containing exactly $k$ points from a given set $S$. · Erdos101.linesWithPointsFor

lintDocstring def

def lintDocstring (location : Syntax) (text : String) : CommandElabM Unit · LatexDocstringLinter.lintDocstring

listChromaticNumber def

The list chromatic number $\chi_L(G)$, defined to be the minimal $k$ such that $G$ is $k$-choosable. · Erdos753.listChromaticNumber

littlewoodPolynomial def

The degree-n Littlewood polynomial f_n(z) = ∑_{0 ≤ k ≤ n} ε_k z^k. · Erdos521.littlewoodPolynomial

localCount def

The number of integers strictly between x and x + y with a divisor in (n, 2n). · Erdos450.localCount

localIndependenceMin def

localIndependenceMin G is the minimum over all vertices of the local independence number indepNeighborsCard G v. This equals $\mathrm{lMin}$ from DeLaVina's notation. · WrittenOnTheWallII.GraphConjecture145.localIndependenceMin

LocallyDense def

A graph G on n vertices is (p, q)-locally dense if every set of p of its vertices spans at least q edges of G; equivalently, every induced subgraph on p vertices has at least q edges. · Erdos667.LocallyDense

localMaxima def

The set of local maxima of the sequence f on (a, ∞). Each local maximum is recorded by the first index m of a maximal interval [m, b] on which f is constant, with f strictly smaller at m - 1 and at b + 1. · Erdos692.localMaxima

LocalSchwartzSolution structure

A smooth solution to the NLS equation on the time interval $[-l, l]$. We additionally require that $x ↦ u(t,x)$ is Schwartz for all $t$ in the interval. · NLSCritical.LocalSchwartzSolution

localTransversalBound def

Maximum global transversal size under a local vertex-set constraint. Infinity records that no finite bound works. · Hypergraph.localTransversalBound

LongestCoilInGraph def

The length of the longest induced cycle (or 'coil') in a graph G. · SnakeInBox.LongestCoilInGraph

LongestCoilInTheBox def

The length of the longest coil for the Hypercube n graph. · SnakeInBox.LongestCoilInTheBox

longestPrimeArithmeticProgressions def

The length of the longest arithmetic progression of primes in $\{1,\ldots,n\}$. · Erdos200.longestPrimeArithmeticProgressions

LongestSnakeInGraph def

The length of the longest induced path (or 'snake') in a graph G. · SnakeInBox.LongestSnakeInGraph

LongestSnakeInTheBox def

The length of the longest snake for the Hypercube n graph. · SnakeInBox.LongestSnakeInTheBox

lovaszThetaFunction def

Lovász Theta Function ($\vartheta(G)$). The Lovász theta function is defined as: $$\vartheta(G) = \min \lambda_{\max}(A)$$ where the minimum is taken over all real symmetric (Hermitian) matrices $A$ such that: · SimpleGraph.lovaszThetaFunction

lowDegreeLayer def

The set of vertices of degree at most two. · SimpleGraph.lowDegreeLayer

lower_bound abbrev

A known lower bound to the limit by Leech [Le56], which is $1.56\dots$. · Erdos170.lower_bound

lowerBest def

Current best lower bound [KPS82]. · Erdos507.lowerBest

lowerBest def

Best-known lower bound [Be23, Theorem 3]. · Green27.lowerBest

lowerDensity def

Given a set S in an order β, where all intervals bounded above are finite, we define the lower density of S (relative to a set A) to be the liminf of the partial densities of S (relative to A) for b → ∞. · Set.lowerDensity

lpSum def

The Firey $L_p$-sum $K \oplus_p L$, equation (4) of the source: the body whose support function is $(h_K^p + h_L^p)^{1/p}$. · Arxiv.«2607.03582».lpSum

Ls def

Ls G is the maximum number of leaves over all spanning trees of G. It is defined to be 0 when G is not connected. · SimpleGraph.Ls

lt₂ def

Let $a = (a_1, a_2, a_3)$ and $b = (b_1, b_2, b_3)$ be two triples of integers. Say that $a$ is $2$-less than $b$, or $a <_2 b$, if $a_i < b_i$ for at least two coordinates $i$. · Arxiv.«1609.08688».lt₂

lucas def

Lucas numbers $L(0) = 2, L(1) = 1, L(n) = L(n-1) + L(n-2)$. · OeisA181546.lucas

lucasNumber def

The Lucas numbers $L_0 = 2$, $L_1=1$, $L_{n+2} = L_{n+1}+L_n$ · lucasNumber

lychrelStep def

One step of the Lychrel iteration: n ↦ n + rev10 n. · LychrelNumbers.lychrelStep