Glossary: N

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

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N def

The product of the first k + 1 primes. On erdosproblems.com/235 this is $N_{k+1}=2\cdot 3\cdots p_{k+1}$. The limit as $k\to\infty$ is the same for either indexing. · Erdos235.N

N def

N X δ is the maximum number of points in a closed disc of radius X in the plane such that the distance between any two of them is at least δ away from the nearest integer. · Erdos466.N

N abbrev

Let $N(r)$ be the number of points $(m, n)$ within a circle of radius $r$, where $m$ and $n$ are both integers. · GaussCircleProblem.N

n def

Let $n_k$ be the least $n \ge 2k$ such that all but one of the integers $n - i$ with $0 \le i < k$ divide $\binom{n}{k}$. · Erdos1063.n

n abbrev

An abbreviation for the fixed number of vertices $n$ in the graph. · Erdos904.n

naiveHeight def

The naïve height of an elliptic curve over ℚ. · EllipticCurveRank.RatEllipticCurve.naiveHeight

naiveHeight def

The logarithmic height hₓ of the x-coordinate with value zero at infinity. · WeierstrassCurve.Affine.Point.naiveHeight

namespaceLinter def

The namespace linter checks that every declaration is inside a namespace. · NamespaceLinter.namespaceLinter

natFacToReal def

def natFacToReal (n : ℕ) : ℝ · OeisA258667.natFacToReal

NavierStokesExistenceAndSmoothness structure

A solution (v, p) to the Navier-Stokes equations in n-dimensional space with viscosity $\nu$, initial velocity $u_0$, and external force $f$. · NavierStokes.NavierStokesExistenceAndSmoothness

NavierStokesExistenceAndSmoothnessPeriodic structure

A solution to the Navier-Stokes equations on the $n$-torus $\mathbb{R}^n/\mathbb{Z}^n$. · NavierStokes.NavierStokesExistenceAndSmoothnessPeriodic

NavierStokesExistenceAndSmoothnessRn structure

A solution to the Navier-Stokes equations on all of $\mathbb{R}^n$ with appropriate decay and energy bounds. · NavierStokes.NavierStokesExistenceAndSmoothnessRn

ncard_add_repr def

def ncard_add_repr (A : Set ℕ) (o : ℕ) (n : ℕ) : ℕ · Erdos868.ncard_add_repr

NcardUnrepresentable abbrev

The number of naturals that cannot be written as the sum of finitely many elements of the set $A$, with repetition allowed. · Erdos434.Nat.NcardUnrepresentable

neg def

Negates an outcome, swapping win and loss. Used when switching player perspectives. · CatchUp.Outcome.neg

negativeCount def

The count of negative terms among $a(1)$, ..., $a(N)$. · OeisA117027.negativeCount

neighborsWithin def

The neighbours of v lying inside s. · SimpleGraph.neighborsWithin

neronTateMatrix def

The Gram matrix of the Néron--Tate height pairing on any family of K-rational points. · WeierstrassCurve.Affine.Point.neronTateMatrix

neronTatePairing def

The Néron--Tate height pairing, defined by polarisation of the canonical height. · WeierstrassCurve.Affine.Point.neronTatePairing

networkWeight def

The network weight nw(X) of a topological space X: the least cardinality of a network, plus ℵ₀. · TopologicalSpace.networkWeight

NewMersenneConjectureStatement def

A natural number p satisfies the statement of the New Mersenne Conjecture if whenever two of the following conditions hold, then all three must hold: 1. $2^p-1$ is prime 2. $(2^p+1)/3$ is prime 3. Exists a number k such that $p = 2^k … · Mersenne.NewMersenneConjectureStatement

next def

The least prime occurring among the sums $d + n / d$ for divisors $d$ of $n$. · OeisA167604.next

nextGeneration def

Defines the set of new numbers generated from a set A by the operation $x y - 1$ for $x \neq y$. · Erdos424.nextGeneration

nextn def

def String.nextn (s : String) (p : Pos.Raw) : Nat → Pos.Raw · String.nextn

nextPrime def

Returns the least prime satisfying $k \le p$ · Erdos930.nextPrime

nextTermFn def

The transition function for these sequences: $f(n) = n + 1 + S(n)$. · OeisA105210.nextTermFn

NG def

Minimum size of the neighbourhood of a non-edge of G. · SimpleGraph.NG

nisanExample def

Simple test example. For multiples of four with $n \ge 12$, this Boolean function has block sensitivity strictly greater than its sensitivity. Source: Nisan1989. · StrongSensitivityConjecture.nisanExample

NoConstantPairwiseGcdCoprimeSubsets def

No r-subset has constant pairwise GCD with coprime quotients. · Erdos535.NoConstantPairwiseGcdCoprimeSubsets

NoHomogeneousSet def

The graph G has no clique and no independent set with m vertices. · Erdos78.NoHomogeneousSet

NoIntegralDiophantineFiveTuple abbrev

The statement that there is no integral Diophantine 5-tuple. · DiophantineTuple.NoIntegralDiophantineFiveTuple

NoKInLineFor def

The proposition that the allowed-set size for $k$ and $N$ is $(k - 1) * N$. · Green72.NoKInLineFor

NoLargeBiclique def

Neither G nor its complement contains a balanced complete bipartite graph $K_{k,k}$ on more than m vertices as a (not necessarily induced) subgraph. That is, there are no two disjoint sets of k vertices with $2k > m$ such that every … · Erdos1036.NoLargeBiclique

non_edge_neighborhood_card def

Cardinality of the union of the neighbourhoods of the ends of the non-edge e. · SimpleGraph.non_edge_neighborhood_card

nonacci def

Nonacci number (Fibonacci 9-step number). $F_9(n)$ is defined by the linear recurrence $F_9(n+9) = \sum_{i=0}^8 F_9(n+i)$, with $F_9(0) = \dots = F_9(7) = 0$ and $F_9(8) = 1$. · OeisA107247.nonacci

NonCollinearFor def

We say a subset S of points is non-collinear for $n$ points if it contains no $n$ points that lie on the same line. · EuclideanGeometry.NonCollinearFor

nonCommutingGraph def

The non-commuting graph $\Gamma = \Gamma(G)$ of a group G, with vertices the elements of G and an edge between g and h if and only if g and h do not commute, $gh \neq hg$. · Erdos1098.nonCommutingGraph

NonDividing def

A finite set $A$ of naturals is non-dividing if no $a \in A$ divides the sum of the elements of any nonempty subset $S \subseteq A \setminus \{a\}$. · Erdos131.NonDividing

NonEdgesAreDiagonals def

Each two non-adjacent vertices have exactly two common neighbors. · Conway99Graph.NonEdgesAreDiagonals

nonsingularReduction def

The points with an integral projective representative whose reduction is non-singular. · WeierstrassCurve.Projective.nonsingularReduction

NonSquarefreeProductProp def

A set $A$ has the non-squarefree product property if $ab + 1$ is not squarefree for all $a, b ∈ A$. · Erdos848.NonSquarefreeProductProp

NonTernary def

Say a finite set of natural numbers is non ternary if it contains no 3-term arithmetic progression of the form n, 2n, 3n. · Erdos168.NonTernary

NonTrilinear def

We say a subset A of points in the plane is non-trilinear if it contains no three points that lie on the same line. · EuclideanGeometry.NonTrilinear

NonTrilinearFor def

We say a subset A of points in the plane is ε-non-trilinear if any subset B of A, contains a non-trilinear subset C of size at least ε|B|. · Erdos846.NonTrilinearFor

nontrivialPosZeros def

The nontrivial zeros of the Riemann zeta function with positive imaginary part. Since the nontrivial zeros are closed under complex conjugation, these determine all nontrivial zeros. · RiemannHypothesis.nontrivialPosZeros

nonUniqueSumCount def

The number of integers in $\{1,\ldots,N\}$ which are not representable in exactly one way as the sum of two elements from $A$ (either because they are not representable at all, or because they are representable in more than one way). · Erdos14.nonUniqueSumCount

normalisedAp def

The normalized coefficient $a_p(E)/(2\sqrt{p})$, using the point-counting definition from ModularityConjecture. · SatoTateConjecture.normalisedAp

normalizedError def

The proposed second-order rescaling of g_3(n): (g_3(n) - (log log n / log n) · n) / (n / log n), whose limit is the constant c in the problem. · Erdos796.normalizedError

normalizedGap def

The normalised prime gap $\frac{p_{n+1}-p_n}{\log n}$, where $p_n$ denotes the $n$-th prime. · Erdos5.normalizedGap

NormallyGenerates def

A relator tuple normally generates the free group when the normal closure of its range is the whole free group. Equivalently, the associated balanced presentation presents the trivial group. · AndrewsCurtis.NormallyGenerates

NormalModalLogic structure

A “normal modal logic” L is any Set Formula such that: 1. If K ⊢ φ, then φ ∈ L (L extends K) 2. If φ ∈ L and (φ ~> ψ) ∈ L, then ψ ∈ L (Closed under MP) 3. If φ ∈ L, then □φ ∈ L (Closed under Necessitation) 4. If φ ∈ L, … · Arxiv.«1308.0994».NormalModalLogic

normedGroup def

G as a metric space NormedGroup G with respect to a generating family P. The metric is given by dist g h = ‖g⁻¹ * h‖, where the norm is given by groupNorm. · Group.Generators.normedGroup

NoShortOddCycle def

A graph avoids odd cycles of length $\leq r$ if it contains no odd cycles of length at most $r$. · Erdos740.NoShortOddCycle

NotSumOfFourTetrahedral def

The set of natural numbers that are not a sum of $4$ tetrahedral numbers. · PollocksConjecture.NotSumOfFourTetrahedral

NoUnitFractionTriple def

A finite set $A$ of positive integers admits no solution to $\frac{1}{a} = \frac{1}{b} + \frac{1}{c}$ with $a, b, c$ distinct elements of $A$. · Erdos302.NoUnitFractionTriple

NP def

The class NP is the set of decision problems $L$ such that there exists a polynomial $p$ over ℕ and a poly-time Turing machine computing a relation $R$ where for all $x$, $L(x)$ iff there exists a $w$ of length at most $p (|x|)$ such that … · ComplexityTheory.NP

nthRoot def

def nthRoot (n : ℕ) (r : ℝ) : ℝ · Real.nthRoot

NtupleCondition def

NtupleCondition A n says that the sum of n elements of A determines the summands, counted with multiplicity and up to permutation. · Erdos41.NtupleCondition

num2DenseSublists def

Number of maximal contiguous sublists of divisors of n where each adjacent pair (d_k, d_{k+1}) satisfies d_{k+1} <= 2 * d_k. This is 1 + the number of "jumps" where d_{k+1} > 2 * d_k. · OeisA237271.num2DenseSublists

numberOfCountableModels def

The number of countable models of some L-Theory T up to isomorphism · VaughtConjecture.numberOfCountableModels

NumberOfPebbles def

The number of pebbles of a distribution is the total number summed over all vertices. · PebblingNumberConjecture.NumberOfPebbles

numBmzCorners def

The number of triples $(x, y, g)$ in $G^3$ such that $g \neq e$, and $(x, y), (xg, y), (x, gy)$ are all in $A$. These are called "BMZ corners" by [Au16]. · Green18.numBmzCorners

numCircles def

The number of circles determined by a set of points P in the plane: the number of distinct circles (spheres) passing through at least three of the points of P. (Three distinct points lie on a common circle precisely when they are not … · Erdos506.numCircles

numDigitsBase10 def

Number of digits of a natural number $n$ in base 10 (with 1 digit for 0). · OeisA70823.numDigitsBase10

numLinesWithFourPointMax def

The maximum number of lines containing exactly $4$ points among all sets $S$ of $n$ points in $\mathbb{R}^2$ satisfying the condition that no five points are collinear. · Erdos101.numLinesWithFourPointMax

numMaximalSidonSets def

$A_1(N)$, the number of maximal Sidon subsets of $\{1, \dots, N\}$. · Erdos862.numMaximalSidonSets

numNaiveCorners def

The number of triples $(x, y, g)$ in $G^3$ such that $g \neq e$, and $(x, y), (gx, y), (x, gy)$ are all in $A$. These are called "naive corners" by [Au16]. · Green18.numNaiveCorners

numPrimeFactors def

The number of distinct prime divisors of the order of G. · Arxiv.«2604.08040».numPrimeFactors

numResidues def

The number of distinct residue classes amongst a tuple $(m_0, \dots, m_k)$ for a prime $q$. · HardyLittlewood.Nat.numResidues

numRootsInUnitDisk def

Counts the number of roots of a Kac polynomial in the unit disk with multiplicity. · Erdos522.KacCoefficients.numRootsInUnitDisk

numTransversals def

The number of transversals of a latin square L, defined as the cardinality of the type of column-selectors σ : Fin n → Fin n satisfying IsTransversal L σ. · numTransversals

numTrianglesAtVertex def

The number of triangles (3-cliques) of G incident to vertex v: the number of 3-element cliques containing v. · SimpleGraph.numTrianglesAtVertex

N₀ def

$N_0(r)$ is the smallest $N$ such that every $r$-colouring of $\{1, \ldots, N\}$ has the monochromatic sum-product property. · Green22.N₀