Glossary: S

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

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S abbrev

Let $S(a)$ be the set of primes such that $a$ is a primitive root modulo $p$. · ArtinPrimitiveRootsConjecture.S

S def

One starts with any initial sequence of integers $S₀$, and extends it by repeatedly appending the curling number of the current sequence. · Arxiv.«0912.2382».S

S def

Define the sum $$S(k) := \sum_{h=1}^{k-1}S'(h, k)$$ · Arxiv.«2501.03234».S

S abbrev

Let S x count the number of ordered pairs of positive integers (a, b) with a + b ≤ x such that σ(a) + σ(b) = σ(a + b), where σ is the sum of divisors function. · Erdos1061.S

S abbrev

Let S be the set of non-trivial solutions to the equation n! = a₁! ··· aₖ! such that a₁ ≥ ... ≥ aₖ and n-1 > a₁. · Erdos373.S

S def

def S (n : ℕ) : ℕ · Erdos379.S

S abbrev

abbrev S · Erdos730.S

S def

From [FSS20]: given $A \subseteq G \times G$ and $d \in G$, let $$S_d(A) = \lbrace (x, y) \in G \times G : (x, y), (x + d, y), (x, y + d) \in A \rbrace$$ · Green19.S

S def

$S_n$ is the sum of the first n primes, i.e. $S_n=p_1+\dots+p_n$, $1$-indexed, matching the MathOverflow question. · MathOverflow434111.S

S def

$S(i) = p_i + p_{i+1}$. · OeisA167918.S

S def

def S (G : SimpleGraph α) : ℝ · SimpleGraph.S

s abbrev

Let $s_1 < s_2 < \cdots$ be the sequence of squarefree numbers. · Erdos145.s

s def

The set of numbers $k$ such that $\mathbb{R}^2$ can be red/blue coloured with no pair of red points unit distance apart, and no $k$-term arithmetic progression of blue points with distance 1. · Erdos188.s

s def

The sequence of squarefree numbers, denoted by s as in Erdős problem 208. · Erdos208.erdos208.s

s def

Let $s(n)=\sigma(n)-n=\sum_{\substack{d\mid n\\ d<n}}d$ be the sum of proper divisors function. · Erdos955.s

s def

The partial sum $S(n) = \sum_{k=1}^n a(k)$. · OeisA105565.s

s def

Let $s(n) = \zeta(3) - \sum_{k=1}^{n} 1/k^3$. · OeisA49473.s

S' def

Define the sum $$S'(h, k) := \sum_{j=1}^{k-1}(-1)^{j + 1 + \lfloor \frac{hj}{k}\rfloor}.$$ · Arxiv.«2501.03234».S'

Satisfies def

z lies in the class (n, a). · Erdos1188.Satisfies

SatisfiesBenford def

A sequence of integers satisfies Benford's law if, for every $t \in [1, 10)$, the asymptotic relative frequency of terms whose decimal significand is at most $t$ equals $\log_{10} t$ (Berger-Hill). This is strictly stronger than the law … · OeisA87455.SatisfiesBenford

SatisfiesCohnElkiesScheme def

The structural rules a function must satisfy to successfully pass through the Cohn-Elkies scheme and generate some valid upper bound. · Green42.SatisfiesCohnElkiesScheme

SatisfiesSendovConjecture def

SatisfiesSendovConjecture n states that Sendov's conjecture is true for every polynomial of degree n. · Sendov.Nat.SatisfiesSendovConjecture

satoTateCDF def

The cumulative distribution function of the Sato–Tate measure. For $t \in [-1,1]$, it is given by $$ F(t) = \frac{t\sqrt{1-t^2}+\arcsin t}{\pi}+\frac{1}{2}. $$ Mathlib's definitions of Real.sqrt and Real.arcsin make this expression … · SatoTateConjecture.satoTateCDF

satoTateIntegral def

For $a \le b$, the mass assigned to $[a,b]$ by the Sato–Tate distribution, written in its usual integral form $$ \frac{2}{\pi}\int_a^b \sqrt{1-x^2}\,dx. $$ · SatoTateConjecture.satoTateIntegral

satoTateMeasure def

For $a \le b$, the mass assigned to $[a,b]$ by the Sato–Tate distribution. This is a real-valued interval mass, not a MeasureTheory.Measure object. · SatoTateConjecture.satoTateMeasure

saturationNumber def

The saturation number μ*(G) (also called the lower matching number): the minimum number of edges in a maximal matching of G. · SimpleGraph.saturationNumber

scale def

A scaling to map the unit square to a standard rectangle. · Mathoverflow34145.scale

scaleL def

The scale $L(n)=\exp(\sqrt{\log n\log\log n})$. · scaleL

SchinzelCondition def

Schinzel condition A condition on sets of polynomials in the Schinzel and Bunyakovsky conjectures. Holds if for every prime $p$ there exists a natural $n$ such that for every polynomial $f$ in the set, $p$ does not divide $f(n)$. · SchinzelCondition

SecondHardyLittlewoodConjectureFor def

Wikipedia URL: https://en.wikipedia.org/wiki/Second_Hardy%E2%80%93Littlewood_conjecture ## Second Hardy-Littlewood Conjecture · HardyLittlewood.SecondHardyLittlewoodConjectureFor

secondKindTerm def

The nth term generated from p by the second-kind recurrence q ↦ 2q - 1. · CunninghamChain.secondKindTerm

secondSmallestDegree def

The second-smallest degree of G's degree sequence — DeLaVina's σ(G) per the WOWII definitions popup (defEntry 65): "order the degree sequence in nondecreasing order d₁ ≤ d₂ ≤ … ≤ dₙ, the second smallest degree of the sequence is … · SimpleGraph.secondSmallestDegree

SegmentsDisjoint def

Two segments are disjoint if they only intersect at their endpoints (if at all). · Erdos1071.SegmentsDisjoint

sensitivity def

Global sensitivity s(f), maximum sensitivity of f over all inputs. · StrongSensitivityConjecture.sensitivity

sensitivityAt def

Local sensitivity s(f,x), number of indices where flipping one bit changes the value of f. · StrongSensitivityConjecture.sensitivityAt

separatedSets def

The sets of $n$ points in $\mathbb{R}^2$ whose pairwise distances are all at least $1$. · Erdos103.separatedSets

seq def

The counterexample sequence: a 0 is a prime at least f 0, and a (k + 1) is a prime larger than a k and f (k + 1) with (k + 1) + a (k + 1) composite. · Erdos1209.seq

seq' def

The counterexample sequence for the squarefree variant. · Erdos1209.seq'

sequenceProduct def

We define the product $\otimes$ of two sequences $(a_i, b_i, c_i)$ and $(d_i, e_i, f_i)$ by the sequence $((a_i, d_j), (b_i, e_j), (c_i, f_j))$, where the indices $(i, j)$ are arranged lexicographically, and the pairs are also ordered … · Arxiv.«1609.08688».sequenceProduct

sequencesCountedByA052709 def

The set of sequences of length $n-1$ satisfying the conditions of the conjecture. · OeisA52709.sequencesCountedByA052709

sequenceSet def

The sequence of sets $A_n$ where $A_0 = \{2, 3\}$ and $A_{n+1}$ is $A_n$ union all newly generated elements. · Erdos424.sequenceSet

sequenceSet def

The set of all terms generated by the sequence starting at $k$. · OeisA105210.sequenceSet

sequenceStartingAt def

The sequence starting at positive integer $k$, where seq $k$ $n$ is the $n$-th term (1-indexed). This is the general form of the sequence A105210 for a starting value $k$. · OeisA105210.sequenceStartingAt

series def

The sum $\sum_{n=1}^\infty \frac{1}{[a_0,\ldots,a_{n - 1}]}$. · Erdos269.series

series def

The series $\sum_{n\geq 1} \frac{1}{(n+1)\cdots (n+f(n))}$, indexed from $0$. · Erdos270.series

setNeighborhood def

DeLaViña's N(S): the union of open vertex neighborhoods. This may intersect S. · WrittenOnTheWallII.GraphConjecture430a.setNeighborhood

setOfPointsModN def

The set of points on an elliptic curve over ZMod n. · ModularityConjecture.setOfPointsModN

setProd def

The set of all products of elements from a Finset S. · OeisA194806.setProd

sharedSet def

The finite set of shared vertices. · Erdos19.EFLConfig.sharedSet

Shatters def

A set family 𝒜 shatters a set A if restricting 𝒜 to A gives rise to all subsets of A. · Shatters

shift def

The left shift of x : G → A by g : G, defined by (shift g x)(h) = x(g⁻¹ * h). This is the standard left shift action of G on A^G. We define it as a plain function rather than a MulAction instance to avoid conflict with the … · GottschalkSurjunctivity.shift

ShiuTheorem def

The statement of Shiu's theorem: for any $k \geq 1$ and $(a, q) = 1$ there exist infinitely many $k$-tuples of consecutive primes $p_m, \dots, p_{m + k - 1}$ all of which are congruent to $a$ modulo $q$. · Erdos427.ShiuTheorem

sicOverlapSq def

The squared overlap value of a SIC family in dimension $d$. · OpenQuantumProblem23.sicOverlapSq

sidonUpperDensity def

The upper density of a Sidon set A, normalized by √N. · Erdos329.sidonUpperDensity

sievedSet def

The set of positive integers not divisible by any element of A. · Erdos489.sievedSet

sign def

true encodes the sign +1, false the sign -1. · Erdos521.sign

signDiffHom def

The group homomorphism $(\sigma_1, \sigma_2) \mapsto \mathrm{sgn}(\sigma_1) \cdot \mathrm{sgn}(\sigma_2)^{-1}$ from $\mathrm{S}_m \times \mathrm{S}_n$ to $\{+1, -1\}$. · Arxiv.«2605.12342».signDiffHom

signedSumCount def

The number of sign patterns $\epsilon \in \{-1,1\}^n$ with $\lvert \epsilon_1z_1+\cdots+\epsilon_nz_n\rvert \leq r$. · Erdos395.signedSumCount

significand def

The decimal significand of an integer x: the unique real number $S(x) \in [1, 10)$ such that $|x| = S(x) \cdot 10^k$ for some integer $k$, with the convention $S(0) = 0$. · OeisA87455.significand

signWeight def

Parity sign of binary weight: $+1$ if popcount is odd, $-1$ if even. · OeisA130911.signWeight

similarityMatrix def

The similarity matrix $Z(t)_{ij} = e^{-t \cdot d(x_i, x_j)}$ of a finite metric space. · Arxiv.«2607.05349».similarityMatrix

SimultaneousDoubleProduct def

The simultaneous double product property [CKS05, 4.1]. · Green36.SimultaneousDoubleProduct

sizeRamsey def

The size Ramsey number r̂(G, H) is the minimum number of edges in a graph F such that any 2-coloring of F's edges contains a copy of G in one color or H in the other. · SimpleGraph.sizeRamsey

sizeRamseyNumber abbrev

The size Ramsey number $\hat{R}(G)$ of G: the least number of edges of a graph which is Ramsey for G. · Erdos720.sizeRamseyNumber

smallestCollection def

Let $$N(a, b)$$, denoted here by smallestCollection a b be the minimal k such that there exist integers $1 < n_1 < n_2 < \dots < n_k$ with $$\frac{a}{b} = \sum_{i=1}^k \frac{1}{n_i}$$ · Erdos304.smallestCollection

smallestCollectionTo def

Write $$N(b) = max_{1 \leq a < b} N(a, b)$$. · Erdos304.smallestCollectionTo

SmoothConjectureFor def

The predicate that the smooth Poincaré conjecture holds in dimension $n$, i.e. that any smooth $n$-dimensional manifold that is homotopy equivalent to the sphere is in fact diffeomorphic to the sphere. As in ConjectureFor, the manifold … · PoincareConjecture.SmoothConjectureFor

smoothGL def

The ℂ-submodule of C^∞ functions on GL n ℝ, which is what the Lie algebra and hence the universal enveloping algebra acts on. · Matrix.GeneralLinearGroup.smoothGL

SmoothTrueValues def

The values at which the smooth version of the conjecture is known to hold. · PoincareConjecture.SmoothTrueValues

snd_gt_half_fst abbrev

The filter on $\mathbb{R} \times \mathbb{R}$ corresponding to sending $x \to \infty$ subject to $x/2 < y < x$ · Erdos1138.snd_gt_half_fst

SO3 abbrev

abbrev SO3 · Rupert.SO3

sofaConstant def

The sofa constant is the maximal area of a moving sofa. · MovingSofa.sofaConstant

sofaOfRotateTranslatePath def

The sofa according to a rotation path $p : [0, \pi/2] \to \mathbb{R}^2$ as in [Ge92] is the intersection over $\alpha \in [0, \pi/2]$ of hallways each translated by $p(\alpha)$ and then rotated by $\alpha$, with the special cases that the … · MovingSofa.sofaOfRotateTranslatePath

SolutionFree def

A set has no solution to $x + 3y = 2z + 2w$ in distinct elements. · Green16.SolutionFree

solutions def

The set of pairs (n, k) representing the solutions to the equation Nat.choose n k = t for a given t, under the constraint 1 ≤ k < n. · Singmaster.solutions

solutionSet def

The set of integer solutions to $x^x y^y = z^z$ with $x, y, z > 1$. · Erdos674.solutionSet

solutionSet def

def solutionSet (n k : ℕ) : Set (Multiset ℕ) · Erdos979.solutionSet

sortedDivisorsList def

def sortedDivisorsList (n : ℕ) : List ℕ · OeisA237271.sortedDivisorsList

sortedTotatives def

The reduced residues 1 ≤ m < n with (m, n) = 1, in increasing order. · Erdos220.sortedTotatives

souslinNumber def

The Souslin number of a topological space is the supremum of the cardinalities of its cellular families. · WeaklyFirstCountable.souslinNumber

sparseConfigurationThreshold def

Least vertex count forcing the Brown--Erdős--Sós little-o conclusion. Infinity records the absence of a finite threshold. · Hypergraph.sparseConfigurationThreshold

SparseImpliesPropertyB def

SparseImpliesPropertyB t c asserts that every finite family F of finite sets, all of size at least t, such that for every nonempty finite set X there are < c * |X| many A ∈ F with A ⊆ X, has property B. · Erdos1022.SparseImpliesPropertyB

spectralPair def

(Ω, Λ) is called a spectral pair if Ω is a (Lebesgue) measurable set of positive finite measure and Λ is a spectrum for Ω, i.e. a set Λ of frequencies such that the associated exponential characters form an orthogonal basis of L^2(Ω). · spectralPair

spectralProductImpliesRightSpectral def

Spectrality of a product with an n-dimensional convex body forces spectrality of its bounded, measurable m-dimensional right factor. · SpectralSetProduct.spectralProductImpliesRightSpectral

Spectrum def

The spectrum of a sequence $(x_n)_{n \ge 1}$ of real numbers is the set of irrational real numbers $\theta \in (0, 1)$ such that the sequence $(x_n - n\theta)_{n \ge 1}$ is not uniformly distributed modulo one. · Bugeaud04.Spectrum

splitByFun def

Split an array into preimages of a function. · ProblemAttributes.splitByFun

Splitting structure

A splitting of a vector bundle 𝓕 is a non-trivial direct sum decomposition of 𝓕 · AlgebraicGeometry.Scheme.VectorBundles.Splitting

sqrtPartialDensity def

The partial density of a Sidon set A up to N, normalized by dividing by √N instead of N. This measures how close the set comes to the optimal density for Sidon sets. · Erdos329.sqrtPartialDensity

Square def

A square of a particular side length as a subset of the Euclidean plane. Not including border, so that squares that touch at the border are disjoint, but a square internal to another shape is a subset of that shape. · SquarePacking.Square

squarefreePart def

n.squarefreePart is the unique a₀ : ℕ such that a₀ is squarefree and n = a₀ * b ^ 2, for some b : ℕ. At 0 this property is not well defined because b must be 0 and a₀ can be any squarefree number; we give the junk value … · Nat.squarefreePart

squareMaximumDegreeVertices def

The maximum-degree vertices of G², presented using finite graph distance. · WrittenOnTheWallII.GraphConjecture172.squareMaximumDegreeVertices

squareMaximumDegreeVertices def

The maximum-degree vertices of G², presented using finite graph distance. · WrittenOnTheWallII.GraphConjecture176.squareMaximumDegreeVertices

squarePart def

The square part is the value of b ^ 2 in the squarefree decomposition of n = a₀ * b ^ 2. · Nat.squarePart

squarePartialProducts def

The number of partial products $a_1, a_1a_2, \ldots, a_1\cdots a_k$ of a finite sequence a = [a₁, …, a_k] which are squares. · Erdos437.squarePartialProducts

squarePeripheryAverage def

The average degree, in G², of the maximum-eccentricity vertices of G². · WrittenOnTheWallII.GraphConjecture181.squarePeripheryAverage

squareRoot def

def squareRoot (N : ℕ) : ℝ · Erdos14.squareRoot

SquareSumFree def

A finite set of natural numbers is square-sum-free if the sum of any two of its elements (possibly equal) is not a square. · Erdos438.SquareSumFree

StandardCube def

The standard cube in $\mathbb{F}_p^n$ is the set of points with coordinates in $\{0, 1\}$. · Green26.StandardCube

standardRelators def

The standard relator tuple, consisting of the free generators themselves. · AndrewsCurtis.standardRelators

Star5 abbrev

Star5: Star graph with center 0 and 5 leaves. · WrittenOnTheWallII.Test.Star5

stars_with_answer_sorry_iff def

Helper to check for answer(sorry) ↔ ... · AnswerLinter.stars_with_answer_sorry_iff

startPos def

The empty starting position on $\{2, \dots, n\}$. · Erdos872.startPos

State structure

The recursive state records the latest term and the product of all official terms so far. · OeisA67836.State

state def

The state after n official terms, with the empty state initialized by term and product one. · OeisA67836.state

state def

The Rule 30 evolution from the single-black-cell initial condition: state 0 is black exactly at position $0$, and each subsequent row is obtained by applying step. · Rule30.state

StateVector abbrev

A state vector in the $d$-dimensional complex Hilbert space $\mathbb{C}^d$. · OpenQuantumProblem23.StateVector

StateVector abbrev

A state vector in the computational basis, viewed as a finite-dimensional Hilbert space. · OpenQuantumProblem35.StateVector

SteinerSystem structure

An $S(t, k, n)$-Steiner system is a collection of $k$-element subsets (called blocks) of $\{0, \ldots, n-1\}$ such that every $t$-element subset is contained in exactly one block. · SteinerSystems.SteinerSystem

step def

The Rule 30 local update on a bi-infinite row row : ℤ → Bool. The new value at position $i$ is row (i-1) ⊕ (row i ∨ row (i+1)), i.e. Wolfram's rule $30$. · Rule30.step

step def

Execution semantics of the Turing machine. · Turing.BusyBeaver.Machine.step

Stmt structure

A Turing machine "statement" is just a command to write a symbol on the tape (at the current position) and then move left or right. · Turing.BusyBeaver.Stmt

stollBinary def

Zero-based form of the Rabinowitz–Gilbert/Stoll binary recurrence: stollBinary t k is the paper's $u_{k+1}$. At $t = \sqrt{2}$ both coefficients equal $\sqrt{2}$, and this is the sequence a shifted by one. · Erdos482.stollBinary

StrictCoveringSystem structure

We say a covering system is strict if all the congruence relations that define it are take modulo a different ideal (or number). · StrictCoveringSystem

strictSublevelSet def

The strict sublevel set $\{ z: \lvert f(z)\rvert< c\}$ of a polynomial $f\in\mathbb{C}[x]$. · Erdos1047.strictSublevelSet

Strongly2Primitive def

A finite set A ⊆ ℕ is strongly 2-primitive if a ∤ b * c whenever a, b, c ∈ A with a ≠ b and a ≠ c. · Erdos793.Strongly2Primitive

stronglyExplicitGraph def

The graph on Fin n described by an adjacency oracle adj which receives n in binary. Two distinct vertices u and v are adjacent if adj (n, u, v) or adj (n, v, u) is true. · Erdos78.stronglyExplicitGraph

stubLinter def

The stub linter checks that no opaque, axiom, or def ... := sorry definitions are present. · StubLinter.stubLinter

subfamilyTransversalBound def

Global transversal bound for a uniform family whose small subfamilies have small transversals. Subfamilies with fewer than q edges are included. · Hypergraph.subfamilyTransversalBound

SubfamilyUnionFree def

A family F of finsets is subfamily union-free if no member is the union of a nonempty subfamily of the others. This is the arbitrary-subfamily strengthening of UnionFree, which only rules out unions of two members. · Finset.SubfamilyUnionFree

subgraphEdgeDistsToBipartite def

For a graph G and a number n, this is the set of minEdgeDistToBipartite A for all induced subgraphs A of G on n vertices. · Erdos74.SimpleGraph.subgraphEdgeDistsToBipartite

SubjectTag structure

structure SubjectTag · ProblemAttributes.SubjectTag

sublevelSet def

The sublevel set $\{ z: \lvert f(z)\rvert\leq c\}$ of a polynomial $f\in\mathbb{C}[x]$. · Erdos1047.sublevelSet

subseqSums' def

The set of subset sums of a sequence ℕ → M, where repetition is allowed. · subseqSums'

subsetSumAvoidanceNumber def

For fixed $c$ and $n$, this is the size of the largest set $A \subseteq \{1, \ldots, \lfloor cn \rfloor\}$ such that no subset of $A$ sums to $n$. · Erdos361.subsetSumAvoidanceNumber

subsetSums def

The set of subset sums of a set A ⊆ M. · subsetSums

subsetSumThreshold def

The subset sum threshold $h(n)$, for each positive $n$, is the maximal separating cardinality of subset sums for $n$. · Erdos789.subsetSumThreshold

subst def

Formula.subst σ φ is the uniform substitution of σ n for each propositional variable Atom n in φ. · Arxiv.«1308.0994».Formula.subst

subwordAt def

A subword (factor) of length n starting at position i. · OeisA6697.subwordAt

subwordsOfLength def

The set of all distinct subwords of length n in the infinite word. · OeisA6697.subwordsOfLength

successProbability def

The probability that a uniformly random k-element subset of G is ε-balanced. · Erdos1179.successProbability

sumConv def

The sum convolution of two functions f, g : ℕ → R, also known as the Cauchy product. (f ∗ g) n = ∑_{a+b=n} f(a)g(b). · AdditiveCombinatorics.sumConv

sumDigits def

The sum of the decimal digits of a natural number. · OeisA100800.sumDigits

sumDivisorInvConsecutiveDifference abbrev

The sum $\sum_{1 \le i < \tau(n)} \frac{1}{d_{i + 1} - d_i}$ over consecutive divisors of $n$. · Erdos884.sumDivisorInvConsecutiveDifference

sumDivisorInvPairwiseDifference abbrev

The sum $\sum_{1 \le i < j \le \tau(n)} \frac{1}{d_j - d_i}$ over all pairs of divisors $d_i < d_j$ of $n$. · Erdos884.sumDivisorInvPairwiseDifference

sumInvPrimesNotDvdCentralBinom abbrev

The sum of the inverses of all primes smaller than $n$, which don't divide the central binom coefficient. · Erdos377.sumInvPrimesNotDvdCentralBinom

summand def

The summand $\frac{1}{n^{1+it}}$, for a natural number $n$ and $t\in\mathbb{R}$. · Erdos967.summand

sumMultiset def

For a finite set $A \subset \mathbb{C}$ and $k \ge 1$, define $A_k$ as the multiset consisting of all sums of $k$ distinct elements of $A$. · Erdos494.sumMultiset

SumOfConsecutiveFree def

A sequence $a : \mathbb{N} \to \mathbb{N}$ is "sum-of-consecutive-free" if no term equals the sum of a contiguous block of earlier terms. That is, for all $i$, $a_i \neq a_j + a_{j+1} + \cdots + a_k$ for any $j \leq k < i$. · Erdos839.SumOfConsecutiveFree

SumOfRPowerful def

Helper Property: $n$ is the sum of at most $r+1$ numbers, each of which is $r$-full. · Erdos1107.SumOfRPowerful

sumPrimeAndTwoPows abbrev

The set of natural numbers that can be written as a sum of a prime and at most $k$ powers of $2$. · Erdos10.sumPrimeAndTwoPows

sumRelevantPrimeFactors def

The sum of distinct prime factors of $n$ that are strictly less than $n$. · OeisA105210.sumRelevantPrimeFactors

sumRep def

The number of sum representations is the sum convolution of A's indicator function with itself: $1_A\ast 1_A(n)$. · AdditiveCombinatorics.sumRep

sumsAndProducts def

The integers which are either the sum or the product of (one or more) distinct elements of A. · Erdos53.sumsAndProducts

sumsOfDistinctPowers def

The set of integers which are the sum of distinct powers d ^ i with i ≥ k. · Erdos124.sumsOfDistinctPowers

sumSquaredGaps def

The sum of the squared differences of adjacent entries of a list of natural numbers. · Erdos220.sumSquaredGaps

sup_primeGap def

The maximal prime gap below $x$, i.e. $d(x) = \max_{p_n < x}(p_{n+1} - p_n)$, where $p_n$ denotes the $n$-th prime. · Erdos1138.sup_primeGap

supp def

The support of a Boolean-valued function: supp v = {i | v i = true}. · DedekindNumber.supp

supportFn def

The support function of a set S with respect to a linear functional a: sup_{φ ∈ S} Re ⟨a, φ⟩. · Green57.supportFn

supportFunction def

The support function $h_K(u) = \sup_{x \in K} \langle x, u\rangle$. · Arxiv.«2607.03582».supportFunction

symAsmRows def

All vertically symmetric alternating sign matrix rows of length 2 * n + 1. · OeisA109074.symAsmRows

symbol def

The symbol {a 0, …, a (n - 1)} = {a 0} ⋯ {a (n - 1)} of an n-tuple of units. · MilnorK.symbol

symbolLengthBounds def

The set of m such that every element of K^M_n(F)/ℓ is a sum of at most m symbols. Its least element, when it exists, is the symbol length of K^M_n(F)/ℓ. · MilnorK.symbolLengthBounds

szeged_aux def

Auxiliary function for Szeged index: counts vertices closer to u than v. · SimpleGraph.szeged_aux

szegedIndex def

The Szeged index of G. · SimpleGraph.szegedIndex